forked from sdr/libosmo-dsp
609 lines
15 KiB
C
609 lines
15 KiB
C
/*
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* cxvec_math.c
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*
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* Complex vectors math and signal processing
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*
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* Copyright (C) 2011 Sylvain Munaut <tnt@246tNt.com>
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*
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* All Rights Reserved
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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/*! \addtogroup cxvec_math
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* @{
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*/
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/*! \file cxvec_math.c
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* \brief Osmocom Complex vectors math implementation
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*/
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#include <complex.h>
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <osmocom/dsp/cxvec.h>
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#include <osmocom/dsp/cxvec_math.h>
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/*! \brief Scale a complex vector (multiply by a constant)
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* \param[in] in Input complex vector
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* \param[in] scale Factor to apply to each sample
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* \param[out] out Output complex vector
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* \returns The output complex vector (or NULL if error)
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*
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* \f$out(k) = in(k) \cdot scale\f$
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*
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* The output vector parameter 'out' can be NULL to allocate a new
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* vector, or can be equal to the 'in' input vector to perform the
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* transform in-place. If it's different, it must be long enough
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* to contain the result (i.e. in->len)
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*/
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struct osmo_cxvec *
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osmo_cxvec_scale(const struct osmo_cxvec *in, float complex scale,
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struct osmo_cxvec *out)
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{
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int i;
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int seq_real;
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seq_real = !!(in->flags & CXVEC_FLG_REAL_ONLY);
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if (!out)
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out = osmo_cxvec_alloc(in->len);
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else if (out->max_len < in->len)
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return NULL;
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if (cimagf(scale) == 0.0f)
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{
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float scalef = crealf(scale);
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if (seq_real) {
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for (i=0; i<in->len; i++)
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out->data[i] = crealf(in->data[i]) * scalef;
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} else {
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for (i=0; i<in->len; i++)
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out->data[i] = in->data[i] * scalef;
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}
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}
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else
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{
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if (seq_real) {
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for (i=0; i<in->len; i++)
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out->data[i] = crealf(in->data[i]) * scale;
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} else {
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for (i=0; i<in->len; i++)
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out->data[i] = in->data[i] * scale;
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}
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out->flags &= ~CXVEC_FLG_REAL_ONLY;
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}
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out->len = in->len;
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return out;
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}
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/*! \brief Rotate a complex vector (frequency shift)
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* \param[in] in Input complex vector
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* \param[in] rps Rotation to apply in radian per sample
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* \param[out] out Output complex vector
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* \returns The output complex vector (or NULL if error)
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*
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* \f$out(k) = in(k) \cdot e^{j \cdot rps \cdot k}\f$
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*
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* The output vector parameter 'out' can be NULL to allocate a new
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* vector, or can be equal to the 'in' input vector to perform the
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* transform in-place. If it's different, it must be long enough
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* to contain the result (i.e. in->len)
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*/
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struct osmo_cxvec *
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osmo_cxvec_rotate(const struct osmo_cxvec *in, float rps,
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struct osmo_cxvec *out)
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{
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int i;
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if (!out)
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out = osmo_cxvec_alloc(in->len);
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else if (out->max_len < in->len)
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return NULL;
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for (i=0; i<in->len; i++)
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out->data[i] = in->data[i] * cexpf(I*(rps*i));
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out->len = in->len;
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out->flags &= ~CXVEC_FLG_REAL_ONLY;
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return out;
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}
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/*! \brief Fractionally delay a vector while maintaining its length
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* \param[in] in Input complex vector
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* \param[in] delay The fractional delay to apply
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* \param[out] out Output complex vector
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* \returns The output complex vector (or NULL if error)
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*
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* The output always has the same length. Samples pushed out by
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* the delays are lost and new ones filled with zeroes are pushed in.
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*
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* The output vector parameter 'out' can be NULL to allocate a new
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* vector, or can be equal to the 'in' input vector to perform the
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* transform in-place. If it's different, it must be long enough
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* to contain the result (i.e. in->len)
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*/
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struct osmo_cxvec *
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osmo_cxvec_delay(const struct osmo_cxvec *in, float delay,
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struct osmo_cxvec *out)
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{
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int ofs_int = (int) roundf(delay);
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float ofs_frac = delay - ofs_int;
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const struct osmo_cxvec *shifted_vect = NULL;
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int i, j;
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/* Get output vector */
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if (!out)
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out = osmo_cxvec_alloc(in->len);
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else if (out->max_len < in->len)
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return NULL;
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/* Set output length / flags */
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out->len = in->len;
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out->flags = in->flags;
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/* Fractional offset (if reasonable) */
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if (fabs(ofs_frac) > 0.05f) {
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float complex _d[21];
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struct osmo_cxvec _sinc_vect, *sinc_vect = &_sinc_vect;
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/* Create sinc vector */
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osmo_cxvec_init_from_data(sinc_vect, _d, 21);
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for (i=0; i<21; i++)
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sinc_vect->data[i] = osmo_sinc(M_PIf * (i - 10.0f - ofs_frac));
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sinc_vect->flags |= CXVEC_FLG_REAL_ONLY;
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/* Convolve */
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shifted_vect = osmo_cxvec_convolve(sinc_vect, in, CONV_NO_DELAY, NULL);
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}
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if (!shifted_vect) /* Also covers failure of convolve ... */
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shifted_vect = in;
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/* Integer offset */
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if (ofs_int < 0) {
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ofs_int = - ofs_int;
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for (i=0; i<(shifted_vect->len-ofs_int); i++)
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out->data[i] = shifted_vect->data[i+ofs_int];
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for (; i<in->len; i++)
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out->data[i] = 0.0f;
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} else {
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for (i=in->len-1,j=shifted_vect->len-1; i>=ofs_int; i--, j--)
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out->data[i] = shifted_vect->data[j-ofs_int];
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for (; i>=0; i--)
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out->data[i] = 0.0f;
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}
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/* Release */
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if (in != shifted_vect)
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osmo_cxvec_free((struct osmo_cxvec *)shifted_vect);
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return out;
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}
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/*! \brief Convolve two complex vectors
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* \param[in] f First input complex vector
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* \param[in] g Second input complex vector
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* \param[in] type The convolution span type
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* \param[out] out Output complex vector
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* \returns The output complex vector (or NULL if error)
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*
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* The convolution of discrete sequences is defined as :
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*
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* \f$(f * g)[n] = \sum_{m=-\infty}^{\infty} f[m] \; g[n-m]\f$
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*
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* Altough the mathematical operation is commutative, the constraint
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* of implementation limit this method. Depending on the type of span
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* chosen, it might not be and it's always recommended that 'g' be the longer
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* sequence. It should not be much of a limitation when this methos is used
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* for filtering or pulseshaping : use 'f' as the filter and 'g' as the
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* signal.
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*
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* The output vector parameter 'out' can be NULL to allocate a new
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* vector. If it's not NULL, it must be long enough to contain the result
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* (length depends on the exact convolution type)
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*/
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struct osmo_cxvec *
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osmo_cxvec_convolve(const struct osmo_cxvec *f, const struct osmo_cxvec *g,
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enum osmo_cxvec_conv_type type, struct osmo_cxvec *out)
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{
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int Lf, Lg, Lo, si, ei, i, jf, jg;
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int f_real, g_real;
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if (!f || !g)
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return NULL;
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f_real = !!(f->flags & CXVEC_FLG_REAL_ONLY);
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g_real = !!(g->flags & CXVEC_FLG_REAL_ONLY);
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/* index / size */
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Lf = f->len;
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Lg = g->len;
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switch (type) {
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case CONV_FULL_SPAN:
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si = 0;
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Lo = Lf + Lg - 1;
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break;
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case CONV_OVERLAP_ONLY:
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si = Lf;
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Lo = abs(Lf-Lg) + 1;
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break;
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case CONV_NO_DELAY:
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si = (Lf >> 1) - ((Lf & 1) ^ 1);
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Lo = Lg;
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break;
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default:
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return NULL;
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}
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ei = si + Lo;
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/* Output vector */
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if (!out)
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out = osmo_cxvec_alloc(Lo);
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else if (out->max_len < Lo)
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return NULL;
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out->flags = 0;
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/* Do the math */
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if (f_real && g_real) {
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for (i=si; i<ei; i++) {
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float sum = 0.0f;
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for (jf=0,jg=i; jf<=Lf && jg>=0; jf++,jg--)
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if (jg < Lg)
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sum += crealf(f->data[jf]) * crealf(g->data[jg]);
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out->data[i-si] = sum;
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}
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out->flags |= CXVEC_FLG_REAL_ONLY;
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} else if (f_real) {
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for (i=si; i<ei; i++) {
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float complex sum = 0.0f;
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for (jf=0,jg=i; jf<Lf && jg>=0; jf++,jg--)
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if (jg < Lg)
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sum += crealf(f->data[jf]) * g->data[jg];
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out->data[i-si] = sum;
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}
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} else if (g_real) {
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for (i=si; i<ei; i++) {
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float complex sum = 0.0f;
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for (jf=0,jg=i; jf<Lf && jg>=0; jf++,jg--)
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if (jg < Lg)
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sum += f->data[jf] * crealf(g->data[jg]);
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out->data[i-si] = sum;
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}
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} else {
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for (i=si; i<ei; i++) {
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float complex sum = 0.0f;
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for (jf=0,jg=i; jf<Lf && jg>=0; jf++,jg--)
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if (jg < Lg)
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sum += f->data[jf] * g->data[jg];
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out->data[i-si] = sum;
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}
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}
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out->len = Lo;
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return out;
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}
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/*! \brief Cross-correlate two complex vectors
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* \param[in] f First input complex vector
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* \param[in] g Second input complex vector
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* \param[in] g_corr_step Allow for oversampling of 'g' compared to 'f'
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* \param[out] out Output complex vector
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* \returns The output complex vector (or NULL if error)
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*
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* The cross-correlation of discrete sequences is defined as :
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*
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* \f$(f \star g)[n] = \sum_{m=-\infty}^{\infty} f^*[m] \; g[n+m]\f$
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*
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* In this implementation, the output vector will be for every n value
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* between 0 and (g->len - f->len + 1). This assumes that g is the longer
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* sequence and we 'fit' f at every positition inside it.
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*
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* With the parameter g_corr_step, it's also possible to have a g sequence
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* that is oversampled with regard to f. (if g_corr_step > 1)
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*
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* The output vector parameter 'out' can be NULL to allocate a new
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* vector. If it's not NULL, it must be long enough to contain the result
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* (i.e. g->len - f->len + 1)
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*/
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struct osmo_cxvec *
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osmo_cxvec_correlate(const struct osmo_cxvec *f, const struct osmo_cxvec *g,
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int g_corr_step, struct osmo_cxvec *out)
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{
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int l, m, n, mn;
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int f_real, g_real;
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f_real = !!(f->flags & CXVEC_FLG_REAL_ONLY);
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g_real = !!(g->flags & CXVEC_FLG_REAL_ONLY);
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l = g->len - (f->len * g_corr_step) + 1;
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if (l < 0)
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return NULL;
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if (!out)
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out = osmo_cxvec_alloc(l);
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else if (out->max_len < l)
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return NULL;
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out->flags = 0;
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if (f_real && g_real) {
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for (m=0; m<l; m++) {
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float v = 0.0f;
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for (n=0,mn=m; n<f->len; n++,mn+=g_corr_step)
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v += crealf(f->data[n]) * crealf(g->data[mn]);
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out->data[m] = v;
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}
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out->flags |= CXVEC_FLG_REAL_ONLY;
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} else if (f_real) {
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for (m=0; m<l; m++) {
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complex float v = 0.0f;
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for (n=0,mn=m; n<f->len; n++,mn+=g_corr_step)
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v += crealf(f->data[n]) * g->data[mn];
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out->data[m] = v;
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}
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} else if (g_real) {
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for (m=0; m<l; m++) {
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complex float v = 0.0f;
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for (n=0,mn=m; n<f->len; n++,mn+=g_corr_step)
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v += f->data[n] * crealf(g->data[mn]);
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out->data[m] = conj(v);
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}
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} else {
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for (m=0; m<l; m++) {
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complex float v = 0.0f;
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for (n=0,mn=m; n<f->len; n++,mn+=g_corr_step)
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v += conj(f->data[n]) * g->data[mn];
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out->data[m] = v;
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}
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}
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out->len = l;
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return out;
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}
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/*! \brief Interpolate any fractional position in a vector using sinc filtering
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* \param[in] cv Input complex vector
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* \param[in] pos Position to interpolate
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*
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* pos must be >= 0 and < cv->len
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*/
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float complex
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osmo_cxvec_interpolate_point(const struct osmo_cxvec *cv, float pos)
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{
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const int N = 10;
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int b, e, i;
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float complex val;
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/* Index */
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i = (int)(floorf(pos));
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b = i - N;
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e = i + N + 1;
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if (b < 0)
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b = 0;
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if (e >= cv->len)
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e = cv->len - 1;
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/* Interpolate */
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if (cv->flags & CXVEC_FLG_REAL_ONLY) {
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float valf = 0.0f;
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for (i=b; i<e; i++)
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valf += crealf(cv->data[i]) * osmo_sinc(M_PIf * (i - pos));
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val = valf;
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} else {
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val = 0.0f;
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for (i=b; i<e; i++)
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val += cv->data[i] * osmo_sinc(M_PIf * (i - pos));
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}
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return val;
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}
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/*! \brief Find the maximum energy (\f$|x|^2\f$) peak in a sequence
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* \param[in] cv Input complex vector
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* \param[in] win_size Size of the window (for algorithms using windows)
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* \param[in] alg Peak detection algorithm to use
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* \param[out] peak_val_p Returns interpolated peak value if non-NULL
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* \returns Peak position with sub-sample accuracy
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*/
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float
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osmo_cxvec_peak_energy_find(const struct osmo_cxvec *cv, int win_size,
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enum osmo_cxvec_peak_alg alg,
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float complex *peak_val_p)
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{
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float val, max_val;
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int idx, max_idx, hi;
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float he[win_size];
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float peak_pos = 0.0f;
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/* Safety */
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if (cv->len < win_size)
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win_size = cv->len;
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/* Scan for the window */
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/* State init */
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val = 0.0f;
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max_val = 0.0f;
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max_idx = 0;
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/* Prefill energy history array */
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for (hi=0; hi<win_size; hi++)
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he[hi] = osmo_normsqf(cv->data[hi]);
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/* Main scan */
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for (idx=0; idx<cv->len-win_size; idx++)
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{
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hi = idx % win_size;
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val -= he[hi];
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he[hi] = osmo_normsqf(cv->data[idx+win_size]);
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val += he[hi];
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if (val > max_val) {
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max_val = val;
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max_idx = idx + 1;
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}
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}
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/* Find maximum peak within the window */
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/* (for PEAK_WEIGH_WIN_CENTER & PEAK_EARLY_LATE */
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if (alg == PEAK_WEIGH_WIN_CENTER || alg == PEAK_EARLY_LATE)
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{
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int mwi = 0;
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float mwv = 0.0f;
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for (idx=max_idx; idx<(max_idx+win_size); idx++) {
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val = osmo_normsqf(cv->data[idx]);
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if (val > mwv) {
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mwv = val;
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mwi = idx;
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}
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}
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if (alg == PEAK_WEIGH_WIN_CENTER) {
|
|
max_idx = mwi - (win_size >> 1);
|
|
|
|
if (max_idx < 0)
|
|
max_idx = 0;
|
|
if (max_idx > (cv->len - win_size - 1))
|
|
max_idx = cv->len - win_size - 1;
|
|
} else {
|
|
max_idx = mwi;
|
|
}
|
|
}
|
|
|
|
/* Find the fractional position */
|
|
if (alg == PEAK_WEIGH_WIN || alg == PEAK_WEIGH_WIN_CENTER)
|
|
{
|
|
float wes = 0.0f;
|
|
float es = 0.0f;
|
|
|
|
for (idx=max_idx; idx<(max_idx+win_size); idx++) {
|
|
val = osmo_normsqf(cv->data[idx]);
|
|
wes += val * idx;
|
|
es += val;
|
|
}
|
|
|
|
peak_pos = wes / es;
|
|
}
|
|
else if (alg == PEAK_EARLY_LATE)
|
|
{
|
|
float early_idx = max_idx - 1.0f;
|
|
float late_idx = max_idx + 1.0f;
|
|
float complex early_pt;
|
|
float complex late_pt;
|
|
float incr = 0.5f;
|
|
|
|
while (incr > (1.0f/1024.0f))
|
|
{
|
|
early_pt = osmo_cxvec_interpolate_point(cv, early_idx);
|
|
late_pt = osmo_cxvec_interpolate_point(cv, late_idx);
|
|
|
|
if (osmo_normsqf(early_pt) < osmo_normsqf(late_pt))
|
|
early_idx += incr;
|
|
else if (osmo_normsqf(early_pt) > osmo_normsqf(late_pt))
|
|
early_idx -= incr;
|
|
else
|
|
break;
|
|
|
|
incr /= 2.0f;
|
|
late_idx = early_idx + 2.0f;
|
|
}
|
|
|
|
peak_pos = early_idx + 1.0f;
|
|
}
|
|
|
|
/* Interpolate peak (if asked to) */
|
|
if (peak_val_p)
|
|
*peak_val_p = osmo_cxvec_interpolate_point(cv, peak_pos);
|
|
|
|
return peak_pos;
|
|
}
|
|
|
|
/*! \brief 'Normalize' an IQ signal and apply decimation/frequency shift
|
|
* \param[in] sig Input complex signal
|
|
* \param[in] decim Decimation factor
|
|
* \param[in] freq_shift Frequency shift in radian per output sample
|
|
* \param[out] out Output complex vector
|
|
* \returns The output complex vector (or NULL if error)
|
|
*
|
|
* The operation performed are DC removal, amplitude normalization (divided
|
|
* by the standard deviation), decimation, frequency shift.
|
|
*
|
|
* The output vector parameter 'out' can be NULL to allocate a new
|
|
* vector, or can be equal to the 'in' input vector to perform the
|
|
* transform in-place. If it's different, it must be long enough to contain
|
|
* the result (i.e. (sig->len + decim - 1) / decim)
|
|
*/
|
|
struct osmo_cxvec *
|
|
osmo_cxvec_sig_normalize(const struct osmo_cxvec *sig,
|
|
int decim, float freq_shift,
|
|
struct osmo_cxvec *out)
|
|
{
|
|
float complex avg = 0.0f;
|
|
float sigma = 0.0f, stddev;
|
|
int l, i, j;
|
|
|
|
l = sig->len / decim;
|
|
|
|
if (!out)
|
|
out = osmo_cxvec_alloc(l);
|
|
else if (out->max_len < l)
|
|
return NULL;
|
|
|
|
for (i=0; i<sig->len; i++)
|
|
avg += sig->data[i];
|
|
avg /= sig->len;
|
|
|
|
for (i=0; i<sig->len; i++)
|
|
sigma += osmo_normsqf(sig->data[i] - avg);
|
|
sigma /= sig->len;
|
|
|
|
stddev = sqrtf(sigma);
|
|
if (stddev == 0.0f)
|
|
stddev = 1.0f; /* Safety against constant signals */
|
|
|
|
for (i=0, j=0; i<l; i++,j+=decim)
|
|
out->data[i] = (sig->data[j] - avg) / stddev;
|
|
|
|
out->len = l;
|
|
out->flags = sig->flags;
|
|
|
|
if (freq_shift != 0.0f)
|
|
for (i=0; i<out->len; i++)
|
|
out->data[i] *= cexpf( I * (freq_shift * i) );
|
|
|
|
return out;
|
|
}
|
|
|
|
/*! @} */
|