fftcoeffs - Frequency-domain coefficients

Syntax

c = fftcoeffs(hd) c = fftcoeffs(ha)

Description

c = fftcoeffs(hd) return the frequency-domain coefficients used when filtering with the dfilt.fftfir object. c contains the coefficients

c = fftcoeffs(ha) return the frequency-domain coefficients used when filtering with adaptfilt objects.

fftcoeffs applies to the following adaptive filter algorithms:

Examples

This example demonstrates returning the FFT coefficients from the discrete-time filter hd.

b = [0.05 0.9 0.05];
len = 50;
hd = dfilt.fftfir(b,len)
 
hd =
 
        FilterStructure: 'Overlap-Add FIR'
              Numerator: [0.0500 0.9000 0.0500]
            BlockLength: 50
    NonProcessedSamples: []
       PersistentMemory: false
 
c=fftcoeffs(hd)

c =

   1.0000          
   0.9920 + 0.1204i
   0.9681 + 0.2386i
   0.9289 + 0.3523i
   0.8753 + 0.4594i
   0.8084 + 0.5580i
   0.7297 + 0.6464i
   0.6408 + 0.7233i
   0.5435 + 0.7874i
   0.4398 + 0.8381i
   0.3317 + 0.8747i
   0.2211 + 0.8971i
   0.1099 + 0.9054i
        0 + 0.9000i
  -0.1070 + 0.8815i
  -0.2097 + 0.8506i
  -0.3066 + 0.8084i
  -0.3967 + 0.7558i
  -0.4790 + 0.6939i
  -0.5528 + 0.6240i
  -0.6176 + 0.5472i
  -0.6730 + 0.4645i
  -0.7185 + 0.3771i
  -0.7541 + 0.2860i
  -0.7796 + 0.1921i
  -0.7949 + 0.0965i
  -0.8000          
  -0.7949 - 0.0965i
  -0.7796 - 0.1921i
  -0.7541 - 0.2860i
  -0.7185 - 0.3771i
  -0.6730 - 0.4645i
  -0.6176 - 0.5472i
  -0.5528 - 0.6240i
  -0.4790 - 0.6939i
  -0.3967 - 0.7558i
  -0.3066 - 0.8084i
  -0.2097 - 0.8506i
  -0.1070 - 0.8815i
        0 - 0.9000i
   0.1099 - 0.9054i
   0.2211 - 0.8971i
   0.3317 - 0.8747i
   0.4398 - 0.8381i
   0.5435 - 0.7874i
   0.6408 - 0.7233i
   0.7297 - 0.6464i
   0.8084 - 0.5580i
   0.8753 - 0.4594i
   0.9289 - 0.3523i
   0.9681 - 0.2386i
   0.9920 - 0.1204i

Similarly, you can use fftcoeffs with the adaptive filters algorithms listed above. Start by constructing an adaptive filter ha.

d  = 16;                    % Number of samples of delay.
b  = exp(j*pi/4)*[-0.7 1];  % Numerator coefficients of channel.
a  = [1 -0.7];              % Denominator coefficients of channel.
ntr= 1000;                  % Number of iterations.
s  = sign(randn(1,ntr+d)) +... 
j*sign(randn(1,ntr+d));     % Baseband QPSK signal.
n  = 0.1*(randn(1,ntr+d) + j*randn(1,ntr+d));  % Noise signal.
r  = filter(b,a,s)+n;       % Received signal.
x  = r(1+d:ntr+d);          % Input signal (received signal).
d  = s(1:ntr);              % Desired signal (delayed QPSK signal).
del = 1;                    % Initial FFT input powers.
mu  = 0.1;                  % Step size.
lam = 0.9;                  % Averaging factor.
d   = 8;                    % Block size.
ha = adaptfilt.pbufdaf(32,mu,1,del,lam,n);

Here are the coefficients before you filter a signal.

c=fftcoeffs(ha)

c =

  Columns 1 through 13 

   0   0   0   0   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0

  Columns 14 through 16 

     0     0     0
     0     0     0
     0     0     0
     0     0     0

Filtering a signal y produces complex nonzero coefficients that you use fftcoeffs to see.

[y,e] = filter(ha,x,d);
c=fftcoeffs(ha)

c =

  Columns 1 through 4 

  0.1425 - 0.0957i  0.0487 - 0.0503i -0.0479 + 0.0315i  0.0769 - 0.0435i
  0.7264 - 0.7605i -0.7423 - 0.6382i  0.1758 + 0.6679i  0.2018 - 0.6544i
  0.1604 + 0.0747i -0.0709 + 0.2610i -0.1634 + 0.2929i -0.1488 + 0.3610i
 -0.0396 + 0.0416i  0.0985 + 0.0095i  0.0733 + 0.0011i  0.0700 + 0.0348i

  Columns 5 through 8 

 -0.0604 + 0.1767i  0.0732 - 0.0648i -0.0870 + 0.0383i  0.0298 - 0.0852i
 -0.1665 + 0.3741i  0.3174 - 0.5234i -0.1990 + 0.4150i  0.3657 - 0.4760i
 -0.2198 + 0.4273i -0.2690 + 0.3981i -0.2820 + 0.3095i -0.3633 + 0.3517i
 -0.0537 - 0.0855i -0.0190 + 0.0336i  0.0091 - 0.0061i -0.0299 + 0.0001i

  Columns 9 through 12 

 -0.0437 + 0.0676i  0.0499 - 0.0164i -0.0397 + 0.0165i  0.0455 - 0.0085i
 -0.3293 + 0.3076i  0.4986 - 0.3949i -0.3300 + 0.3448i  0.5492 - 0.2633i
 -0.2671 + 0.3238i -0.3813 + 0.2999i -0.4130 + 0.2333i -0.2910 + 0.2823i
 -0.0300 + 0.0236i -0.0103 + 0.0438i  0.0244 + 0.0476i  0.1043 + 0.0359i

  Columns 13 through 16 

 -0.0602 + 0.1189i -0.0227 - 0.1076i -0.0282 + 0.0634i  0.0170 - 0.0464i
 -0.4385 + 0.0549i  0.5232 - 0.1904i -0.6414 - 0.1717i  0.5580 + 0.6477i
 -0.4511 + 0.3217i -0.4301 + 0.1765i -0.2805 + 0.1270i -0.2531 + 0.0299i
  0.1076 - 0.0383i -0.0166 + 0.0020i  0.0004 - 0.0376i  0.0071 - 0.0714i

fftcoeffs - Frequency-domain coefficients

Syntax

Description

Examples

See Also