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Miscellaneous SP Functions
[Signal Processing (SP) Module]

Functions

cvec itpp::xcorr (const cvec &x, const cvec &y, const int max_lag=-1, const std::string scaleopt="none")
 Cross Correlation.
cvec itpp::xcorr (const cvec &x, const int max_lag=-1, const std::string scaleopt="none")
 Cross Correlation.
void itpp::xcorr (const cvec &x, const cvec &y, cvec &out, const int max_lag=-1, const std::string scaleopt="none", bool autoflag=true)
 Cross Correlation.
mat itpp::cov (const mat &X, bool is_zero_mean=false)
 Covariance matrix calculation.
vec itpp::spectrum (const vec &v, int nfft=256, int noverlap=0)
 Power spectrum calculation.
vec itpp::spectrum (const vec &v, const vec &w, int noverlap=0)
 Power spectrum calculation.
vec itpp::filter_spectrum (const vec &a, int nfft=256)
 Power spectrum calculation of a filter.
vec itpp::filter_spectrum (const vec &a, const vec &b, int nfft=256)
 Power spectrum calculation of a filter.



void itpp::xcorr_old (const vec &x, const vec &y, vec &out, const int max_lag=-1, const std::string scaleopt="none")
 Cross-correlation calculation.
void itpp::xcorr (const vec &x, const vec &y, vec &out, const int max_lag, const std::string scaleopt)
 Cross-correlation calculation.



vec itpp::xcorr_old (const vec &x, const vec &y, const int max_lag=-1, const std::string scaleopt="none")
 Cross-correlation calculation.
vec itpp::xcorr (const vec &x, const vec &y, const int max_lag, const std::string scaleopt)
 Cross-correlation calculation.



vec itpp::xcorr_old (const vec &x, const int max_lag=-1, const std::string scaleopt="none")
 Auto-correlation calculation.
vec itpp::xcorr (const vec &x, const int max_lag, const std::string scaleopt)
 Auto-correlation calculation.

Function Documentation

void itpp::xcorr_old ( const vec &  x,
const vec &  y,
vec &  out,
const int  max_lag = -1,
const std::string  scaleopt = "none" 
)

Cross-correlation calculation.

z=xcorr(x,y,max_lag), where x and y are length M vectors (M>1), returns the length 2*max_lag+1 cross-correlation sequence z. (lags: -max_lag,...,0,...,max_lag)

For max_lag=-1 the cross-correlation sequence is of length 2*M-1, i.e., the cross-correlation for all possible lags.

Scaling options scaleopt:

  • none => No scaling of the cross-correlation vector
  • biased => Scales the cross-correlation vector by 1/M
  • unbiased => Scales the cross-correlation vector by 1/(M-abs(lag))
  • coeff => Normalises the cross-correlation to 1 for zero lag.
Note:
max_lag <= M-1
If x and y are of different length, the shortest one is zero-padded
Parameters:
x (Input) Vector of samples
y (Input) Vector of samples
out (Output) The cross correlation between x and y.
max_lag (Input) Maximum lag for which the cross-correlation is calculated. The output vector is of size 2*maxlag+1. Default value: max_lag=-1 calculates the cross-correlations for all possible lags
scaleopt (Input) Indicates how the cross-correlation function should be scaled. Default value: "none" indicates that no scaling is done
void itpp::xcorr ( const vec &  x,
const vec &  y,
vec &  out,
const int  max_lag,
const std::string  scaleopt 
)

Cross-correlation calculation.

z=xcorr(x,y,max_lag), where x and y are length M vectors (M>1), returns the length 2*max_lag+1 cross-correlation sequence z. (lags: -max_lag,...,0,...,max_lag)

For max_lag=-1 the cross-correlation sequence is of length 2*M-1, i.e., the cross-correlation for all possible lags.

Scaling options scaleopt:

  • none => No scaling of the cross-correlation vector
  • biased => Scales the cross-correlation vector by 1/M
  • unbiased => Scales the cross-correlation vector by 1/(M-abs(lag))
  • coeff => Normalises the cross-correlation to 1 for zero lag.
Note:
max_lag <= M-1
If x and y are of different length, the shortest one is zero-padded
Parameters:
x (Input) Vector of samples
y (Input) Vector of samples
out (Output) The cross correlation between x and y.
max_lag (Input) Maximum lag for which the cross-correlation is calculated. The output vector is of size 2*maxlag+1. Default value: max_lag=-1 calculates the cross-correlations for all possible lags
scaleopt (Input) Indicates how the cross-correlation function should be scaled. Default value: "none" indicates that no scaling is done
vec itpp::xcorr_old ( const vec &  x,
const vec &  y,
const int  max_lag = -1,
const std::string  scaleopt = "none" 
)

Cross-correlation calculation.

z=xcorr(x,y,max_lag), where x and y are length M vectors (M>1), returns the length 2*max_lag+1 cross-correlation sequence z. (lags: -max_lag,...,0,...,max_lag)

For max_lag=-1 the cross-correlation sequence is of length 2*M-1, i.e., the cross-correlation for all possible lags.

Scaling options scaleopt:

  • none => No scaling of the cross-correlation vector
  • biased => Scales the cross-correlation vector by 1/M
  • unbiased => Scales the cross-correlation vector by 1/(M-abs(lag))
  • coeff => Normalises the cross-correlation to 1 for zero lag.
Note:
max_lag <= M-1
If x and y are of different length, the shortest one is zero-padded
Parameters:
x (Input) Vector of samples
y (Input) Vector of samples
max_lag (Input) Maximum lag for which the cross-correlation is calculated. The output vector is of size 2*maxlag+1. Default value: max_lag=-1 calculates the cross-correlations for all possible lags
scaleopt (Input) Indicates how the cross-correlation function should be scaled. Default value: "none" indicates that no scaling is done
Returns:
The cross correlation between x and y.
vec itpp::xcorr ( const vec &  x,
const vec &  y,
const int  max_lag,
const std::string  scaleopt 
)

Cross-correlation calculation.

z=xcorr(x,y,max_lag), where x and y are length M vectors (M>1), returns the length 2*max_lag+1 cross-correlation sequence z. (lags: -max_lag,...,0,...,max_lag)

For max_lag=-1 the cross-correlation sequence is of length 2*M-1, i.e., the cross-correlation for all possible lags.

Scaling options scaleopt:

  • none => No scaling of the cross-correlation vector
  • biased => Scales the cross-correlation vector by 1/M
  • unbiased => Scales the cross-correlation vector by 1/(M-abs(lag))
  • coeff => Normalises the cross-correlation to 1 for zero lag.
Note:
max_lag <= M-1
If x and y are of different length, the shortest one is zero-padded
Parameters:
x (Input) Vector of samples
y (Input) Vector of samples
max_lag (Input) Maximum lag for which the cross-correlation is calculated. The output vector is of size 2*maxlag+1. Default value: max_lag=-1 calculates the cross-correlations for all possible lags
scaleopt (Input) Indicates how the cross-correlation function should be scaled. Default value: "none" indicates that no scaling is done
Returns:
The cross correlation between x and y.
cvec itpp::xcorr ( const cvec &  x,
const cvec &  y,
const int  max_lag = -1,
const std::string  scaleopt = "none" 
)

Cross Correlation. 

 r = xcorr(x,y)

returns the cross-correlation vector r.

vec itpp::xcorr_old ( const vec &  x,
const int  max_lag = -1,
const std::string  scaleopt = "none" 
)

Auto-correlation calculation.

z=xcorr(x,max_lag), where x and is a length M vector (M>1), returns the length 2*max_lag+1 auto-correlation sequence z. (lags: -max_lag,...,0,...,max_lag)

For max_lag=-1 the auto-correlation sequence is of length 2*M-1, i.e., the cross correlation for all possible lags.

Scaling options scaleopt:

  • none => No scaling of the auto-correlation vector
  • biased => Scales the auto-correlation vector by 1/M
  • unbiased => Scales the auto-correlation vector by 1/(M-abs(lag))
  • coeff => Normalises the auto-correlation so that acf(x)=1 for zero lag.
Note:
max_lag <= M-1
Parameters:
x (Input) Vector of samples
max_lag (Input) Maximum lag for which the auto-correlation is calculated. The output vector is of size 2*maxlag+1. Default value max_lag=-1 calculates the auto-correlations for all possible lags.
scaleopt (Input) Indicates how the auto-correlation function should be scaled. Default value: "none" indicates that no scaling is done.
Returns:
The auto-correlation of x.
vec itpp::xcorr ( const vec &  x,
const int  max_lag,
const std::string  scaleopt 
)

Auto-correlation calculation.

z=xcorr(x,max_lag), where x and is a length M vector (M>1), returns the length 2*max_lag+1 auto-correlation sequence z. (lags: -max_lag,...,0,...,max_lag)

For max_lag=-1 the auto-correlation sequence is of length 2*M-1, i.e., the cross correlation for all possible lags.

Scaling options scaleopt:

  • none => No scaling of the auto-correlation vector
  • biased => Scales the auto-correlation vector by 1/M
  • unbiased => Scales the auto-correlation vector by 1/(M-abs(lag))
  • coeff => Normalises the auto-correlation so that acf(x)=1 for zero lag.
Note:
max_lag <= M-1
Parameters:
x (Input) Vector of samples
max_lag (Input) Maximum lag for which the auto-correlation is calculated. The output vector is of size 2*maxlag+1. Default value max_lag=-1 calculates the auto-correlations for all possible lags.
scaleopt (Input) Indicates how the auto-correlation function should be scaled. Default value: "none" indicates that no scaling is done.
Returns:
The auto-correlation of x.
cvec itpp::xcorr ( const cvec &  x,
const int  max_lag = -1,
const std::string  scaleopt = "none" 
)

Cross Correlation. 

 r = xcorr(x)

returns the auto-correlation vecotr r.

void itpp::xcorr ( const cvec &  x,
const cvec &  y,
cvec &  out,
const int  max_lag = -1,
const std::string  scaleopt = "none",
bool  autoflag = true 
)

Cross Correlation. 

 xcorr(x,y,out)

Computes the cross-correlatin and returns in vector out

mat itpp::cov ( const mat &  X,
bool  is_zero_mean = false 
)

Covariance matrix calculation.

Calculates the covariance matrix of the observations in the matrix $X$. Each row is an observation and each column represents a variable.

The covariance is normalized with the number of observations $N$. The mean value is removed before calculation.

Set is_zero_mean if X already has zero mean.

Referenced by pcamat().

vec itpp::spectrum ( const vec &  v,
int  nfft = 256,
int  noverlap = 0 
)

Power spectrum calculation.

Calculates the power spectrum using the Welch method and a Hanning window.

Referenced by itpp::Punctured_Convolutional_Code::calculate_spectrum(), itpp::Convolutional_Code::calculate_spectrum(), itpp::Punctured_Convolutional_Code::fast(), and itpp::Convolutional_Code::fast().

vec itpp::spectrum ( const vec &  v,
const vec &  w,
int  noverlap = 0 
)

Power spectrum calculation.

Calculates the power spectrum using using the Welch method and the supplied window w.

vec itpp::filter_spectrum ( const vec &  a,
int  nfft = 256 
)

Power spectrum calculation of a filter.

Calculates the power spectrum of a filter with transfer function a(z)

vec itpp::filter_spectrum ( const vec &  a,
const vec &  b,
int  nfft = 256 
)

Power spectrum calculation of a filter.

Calculates the power spectrum of a filter with transfer function a(z)/b(z)

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