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Filter Classes and Functions


Classes

class  itpp::Filter< T1, T2, T3 >
 Virtual Filter Base Class. More...
class  itpp::MA_Filter< T1, T2, T3 >
 Moving Average Filter Base Class. More...
class  itpp::AR_Filter< T1, T2, T3 >
 Autoregressive (AR) Filter Base Class. More...
class  itpp::ARMA_Filter< T1, T2, T3 >
 Autoregressive Moving Average (ARMA) Filter Base Class. More...
class  itpp::Freq_Filt< Num_T >
 Freq_Filt Frequency domain filtering using the overlap-add technique. More...
void itpp::freqz (const cvec &b, const cvec &a, const int N, cvec &h, vec &w)
 Frequency response of filter.
cvec itpp::freqz (const cvec &b, const cvec &a, const int N)
 Frequency response of filter.
cvec itpp::freqz (const cvec &b, const cvec &a, const vec &w)
 Frequency response of filter.
void itpp::freqz (const vec &b, const vec &a, const int N, cvec &h, vec &w)
 Frequency response of filter.
cvec itpp::freqz (const vec &b, const vec &a, const int N)
 Frequency response of filter.
cvec itpp::freqz (const vec &b, const vec &a, const vec &w)
 Frequency response of filter.

Functions

vec itpp::filter (const vec &b, const vec &a, const vec &input)
 ARMA filter function.
cvec itpp::filter (const vec &b, const vec &a, const cvec &input)
cvec itpp::filter (const cvec &b, const cvec &a, const cvec &input)
cvec itpp::filter (const cvec &b, const cvec &a, const vec &input)
vec itpp::filter (const vec &b, const int one, const vec &input)
cvec itpp::filter (const vec &b, const int one, const cvec &input)
cvec itpp::filter (const cvec &b, const int one, const cvec &input)
cvec itpp::filter (const cvec &b, const int one, const vec &input)
vec itpp::filter (const int one, const vec &a, const vec &input)
cvec itpp::filter (const int one, const vec &a, const cvec &input)
cvec itpp::filter (const int one, const cvec &a, const cvec &input)
cvec itpp::filter (const int one, const cvec &a, const vec &input)
vec itpp::filter (const vec &b, const vec &a, const vec &input, const vec &state_in, vec &state_out)
cvec itpp::filter (const vec &b, const vec &a, const cvec &input, const cvec &state_in, cvec &state_out)
cvec itpp::filter (const cvec &b, const cvec &a, const cvec &input, const cvec &state_in, cvec &state_out)
cvec itpp::filter (const cvec &b, const cvec &a, const vec &input, const cvec &state_in, cvec &state_out)
vec itpp::filter (const vec &b, const int one, const vec &input, const vec &state_in, vec &state_out)
cvec itpp::filter (const vec &b, const int one, const cvec &input, const cvec &state_in, cvec &state_out)
cvec itpp::filter (const cvec &b, const int one, const cvec &input, const cvec &state_in, cvec &state_out)
cvec itpp::filter (const cvec &b, const int one, const vec &input, const cvec &state_in, cvec &state_out)
vec itpp::filter (const int one, const vec &a, const vec &input, const vec &state_in, vec &state_out)
cvec itpp::filter (const int one, const vec &a, const cvec &input, const cvec &state_in, cvec &state_out)
cvec itpp::filter (const int one, const cvec &a, const cvec &input, const cvec &state_in, cvec &state_out)
cvec itpp::filter (const int one, const cvec &a, const vec &input, const cvec &state_in, cvec &state_out)
vec itpp::fir1 (int N, double cutoff)
 Design a Nth order FIR filter with cut-off frequency cutoff using the window method.
void itpp::polystab (const vec &a, vec &out)
 Polynomial Stabilization.
vec itpp::polystab (const vec &a)
void itpp::polystab (const cvec &a, cvec &out)
cvec itpp::polystab (const cvec &a)
void itpp::filter_design_autocorrelation (const int N, const vec &f, const vec &m, vec &R)
 Calculate autocorrelation from the specified frequency-response (suitable for filter design).
void itpp::modified_yule_walker (const int m, const int n, const int N, const vec &R, vec &a)
 Estimation of AR-part in an ARMA model given the autocorrelation.
void itpp::arma_estimator (const int m, const int n, const vec &R, vec &b, vec &a)
 Estimation of ARMA model given the autocorrelation.
void itpp::yulewalk (const int N, const vec &f, const vec &m, vec &b, vec &a)
 ARMA filter design using a least-squares fit to the specified frequency-response.

Detailed Description


Function Documentation

vec itpp::filter ( const vec b,
const vec a,
const vec input 
)

ARMA filter function.

These functions implements a autoregressive moving average (ARMA) filter according to

\[ a(0)*y(n) = b(0)*x(n) + b(1)*x(n-1) + \ldots + b(N_b)*x(n-N_b) - a(1)*y(n-1) - \ldots - a(N_a)*y(n-N_a) \]

where a and b are the filter coefficients, x is the input and y is the output.

Setting a=1 gives a MA filter and b=1 gives a AR filter. The length of the output vector equals the length of the input vector. The state vectors state_in and state_out is of length $max(N_a, n_b) - 1$.

If no start state state_in is given it is set to zero.

Definition at line 41 of file filter.cpp.

Referenced by itpp::arma_estimator().

vec itpp::fir1 ( int  N,
double  cutoff 
)

Design a Nth order FIR filter with cut-off frequency cutoff using the window method.

Definition at line 244 of file filter.cpp.

References itpp::hamming(), itpp::length(), itpp::sinc(), and itpp::sum().

void itpp::polystab ( const vec a,
vec out 
)

Polynomial Stabilization.

Author:
Tony Ottosson
Stabilizes the polynomial transfer function by replacing all roots outside the unit cirlce with their reflection inside the unit circle.

Definition at line 47 of file filter_design.cpp.

References itpp::abs(), itpp::conj(), itpp::poly(), itpp::real(), and itpp::roots().

Referenced by itpp::modified_yule_walker(), and itpp::polystab().

void itpp::freqz ( const cvec b,
const cvec a,
const int  N,
cvec h,
vec w 
)

Frequency response of filter.

Author:
Tony Ottosson
Calculates the N-point frequency response of the supplied digital filter over the frequencies w. If w is not given the response is evaluated over the range 0 to $\pi$ with N values. The default value of N is 512.

If w is supplied polyval() is used. Otherwise the calculation is based on the fft.

Definition at line 73 of file filter_design.cpp.

References itpp::elem_div(), itpp::fft(), itpp::linspace(), and itpp::pi.

Referenced by itpp::freqz().

void itpp::filter_design_autocorrelation ( const int  N,
const vec f,
const vec m,
vec R 
)

Calculate autocorrelation from the specified frequency-response (suitable for filter design).

Author:
Tony Ottosson
Calculates the autocorrelation function of size N corresponding to the specified frequency response. Useful as a first step in designing filters.

The vectors f and m is the frequency response. The frequencies should be between 0 and 1.0 (equal to half the sample rate) in increasing order. Both 0.0 and 1.0 must be included. The frequency response is upsampled to 512 points and the autocorrelation is ifft of the power magnitude response of the upsampled frequency response.

Definition at line 155 of file filter_design.cpp.

References itpp::concat(), itpp::floor_i(), itpp::ifft_real(), it_assert, itpp::reverse(), itpp::sqr(), and itpp::to_cvec().

Referenced by itpp::yulewalk().

void itpp::modified_yule_walker ( const int  m,
const int  n,
const int  N,
const vec R,
vec a 
)

Estimation of AR-part in an ARMA model given the autocorrelation.

Author:
Tony Ottosson
Estimates the AR-part of an ARMA model from the given autocorrelation. The AR part is of order n. The overdetermined modified Yule-Walker equations are used.

If $N>n$ then the system is overdetermined and a least squares solution is used. As a rule of thumb use $N = 4 n$

The parameter m is the order of the MA-part such that $R(k) = 0, \forall \|k\| > m$.

The supplied autocorrelation should at least be of size N.

References: Stoica and Moses, Introduction to spectral analysis, Prentice Hall, 1997.

Definition at line 199 of file filter_design.cpp.

References itpp::abs(), itpp::backslash(), itpp::concat(), it_assert, itpp::polystab(), itpp::R, itpp::reverse(), and itpp::toeplitz().

Referenced by itpp::arma_estimator().

void itpp::arma_estimator ( const int  m,
const int  n,
const vec R,
vec b,
vec a 
)

Estimation of ARMA model given the autocorrelation.

Author:
Tony Ottosson
Estimates an ARMA model from the given autocorrelation. The AR part is of order n and the MA part is of order m.

The AR part (the denominator) is calcuated using the modified Yule-Walker equations. The the MA part (the nominator) is calculated by calculating the inverse magnitude spectrum using FFTs of size 512 which is an AR-system. This AR-system is then solved using the Levinson-Durbin algorithm.

The supplied autocorrelation is windowed using a Hamming window of size $2(m+n)$ and hence should at least be of that size.

References: [1] Stoica and Moses, Introduction to spectral analysis, Prentice Hall, 1997. [2] B. Friedlander and B. Porat, The modified Yule-Walker method of ARMA spectral estimation, IEEE Trans. Aerospace and Electronic Systems, Vol. AES-20, No. 2, pp. 158--173, March 1984.

Definition at line 230 of file filter_design.cpp.

References itpp::backslash(), itpp::concat(), itpp::cos(), itpp::elem_div(), itpp::elem_mult(), itpp::exp(), itpp::fft(), itpp::fft_real(), itpp::filter(), itpp::ifft(), it_assert, itpp::linspace(), itpp::log(), itpp::modified_yule_walker(), itpp::pi, itpp::real(), itpp::to_cmat(), itpp::to_cvec(), itpp::toeplitz(), itpp::zeros(), and itpp::zeros_c().

Referenced by itpp::yulewalk().

void itpp::yulewalk ( const int  N,
const vec f,
const vec m,
vec b,
vec a 
)

ARMA filter design using a least-squares fit to the specified frequency-response.

Author:
Tony Ottosson
The arma_estimator() function is used to calculate the a and b coefficients.

The vectors f and m is the frequency response. The frequencies should be between 0 and 1.0 (equal to half the sample rate) in increasing order. Both 0.0 and 1.0 must be included. The filter_design_autocorrelation() fucnction is used to interpolate the frequency response and calculate the corresponding autocorrelation.

Observe: this function will not always give exactly the same result as the matlab yulewalk function.

Definition at line 271 of file filter_design.cpp.

References itpp::arma_estimator(), itpp::filter_design_autocorrelation(), it_assert, and itpp::R.

cvec itpp::freqz ( const cvec b,
const cvec a,
const int  N = 512 
)

Frequency response of filter.

Author:
Tony Ottosson
Calculates the N-point frequency response of the supplied digital filter over the frequencies w. If w is not given the response is evaluated over the range 0 to $\pi$ with N values. The default value of N is 512.

If w is supplied polyval() is used. Otherwise the calculation is based on the fft.

Definition at line 87 of file filter_design.cpp.

References itpp::freqz().

cvec itpp::freqz ( const cvec b,
const cvec a,
const vec w 
)

Frequency response of filter.

Author:
Tony Ottosson
Calculates the N-point frequency response of the supplied digital filter over the frequencies w. If w is not given the response is evaluated over the range 0 to $\pi$ with N values. The default value of N is 512.

If w is supplied polyval() is used. Otherwise the calculation is based on the fft.

Definition at line 98 of file filter_design.cpp.

References itpp::cos(), itpp::elem_div(), max, itpp::polyval(), itpp::sin(), itpp::to_cvec(), and itpp::zero_pad().

void itpp::freqz ( const vec b,
const vec a,
const int  N,
cvec h,
vec w 
)

Frequency response of filter.

Author:
Tony Ottosson
Calculates the N-point frequency response of the supplied digital filter over the frequencies w. If w is not given the response is evaluated over the range 0 to $\pi$ with N values. The default value of N is 512.

If w is supplied polyval() is used. Otherwise the calculation is based on the fft.

Definition at line 113 of file filter_design.cpp.

References itpp::elem_div(), itpp::fft_real(), itpp::linspace(), and itpp::pi.

cvec itpp::freqz ( const vec b,
const vec a,
const int  N = 512 
)

Frequency response of filter.

Author:
Tony Ottosson
Calculates the N-point frequency response of the supplied digital filter over the frequencies w. If w is not given the response is evaluated over the range 0 to $\pi$ with N values. The default value of N is 512.

If w is supplied polyval() is used. Otherwise the calculation is based on the fft.

Definition at line 127 of file filter_design.cpp.

References itpp::freqz().

cvec itpp::freqz ( const vec b,
const vec a,
const vec w 
)

Frequency response of filter.

Author:
Tony Ottosson
Calculates the N-point frequency response of the supplied digital filter over the frequencies w. If w is not given the response is evaluated over the range 0 to $\pi$ with N values. The default value of N is 512.

If w is supplied polyval() is used. Otherwise the calculation is based on the fft.

Definition at line 138 of file filter_design.cpp.

References itpp::cos(), itpp::elem_div(), max, itpp::polyval(), itpp::sin(), itpp::to_cvec(), and itpp::zero_pad().

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