A library with SDR DSP primitives
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libosmo-dsp/src/cxvec_math.c

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