freqsamp

Real or complex frequency-sampled FIR filter from specification object

Syntax

hd = design(d,'freqsamp')
hd = design(...,'FilterStructure',structure)
hd = design(...,'Window',window)


Description

hd = design(d,'freqsamp') designs a frequency-sampled filter specified by the filter specifications object d.

hd = design(...,'FilterStructure',structure) returns a filter with the filter structure you specify by the structure input argument. structure is dffir by default and can be any one of the following filter structures.

Structure	Description of Resulting Filter
dffir	Direct-form FIR filter
dffirt	Transposed direct-form FIR filter
dfsymfir	Symmetrical direct-form FIR filter
dfasymfir	Asymmetrical direct-form FIR filter
fftfir	Fast Fourier transform FIR filter

hd = design(...,'Window',window) designs filters using the window specified in window. Provide the input argument window as

• The window name in single quotes. For example, use 'bartlett', or 'hamming'. See window for the full list of available windows.

• A function handle that references the window function. When the window function requires more than one input, use a cell array to hold the required arguments. The first example shows a cell array input argument.

• The window vector itself.

Examples

Filters with Arbitrary Magnitude Response

Design FIR filters that have arbitrary magnitude responses.

Generate a real filter whose response has three distinct sections:

• A sinusoidal response section for lower frequencies

• A piecewise linear response section for intermediate frequencies

• A quadratic response section for higher frequencies.

b1 = 0:0.01:0.18;
a1 = 0.5+sin(2*pi*7.5*b1)/4;

b2 = [0.2 0.38 0.4 0.55 0.562 0.585 0.6 0.78];
a2 = [0.5 2.3 1 1 -0.2 -0.2 1 1];

b3 = 0.79:0.01:1;
a3 = 0.2+18*(1-b3).^2;

f = [b1 b2 b3];
a = [a1 a2 a3];
n = 300;

Design the filter using a Kaiser window with β = 50.

d = fdesign.arbmag('n,f,a',n,f,a);
hd = design(d,'freqsamp','Window',{@kaiser,50});

[h,w] = freqz(hd);
plot(w/pi,mag2db(abs(h)),f,mag2db(abs(a)),"--")

Design an arbitrary-magnitude complex FIR filter. The vector f contains frequency locations. The vector a contains the desired filter response values at the locations specified in f. Use a rectangular window for the design.

f = [-1 -0.93443 -0.86885 -0.8033 -0.7377 -0.67213 -0.60656 -0.54098 ...
    -0.47541 -0.40984 -0.34426 -0.27869 -0.21311 -0.14754 -0.081967 ...
    -0.016393 0.04918 0.11475 0.18033 0.2459 0.31148 0.37705 0.44262 ...
    0.5082 0.57377 0.63934 0.70492 0.77049 0.83607 0.90164 1];

a = [0.0095848 0.021972 0.047249 0.099869 0.23119 0.57569 0.94032 ...
    0.98084 0.99707 0.99565 0.9958 0.99899 0.99402 0.99978 ...
    0.99995 0.99733 0.99731 0.96979 0.94936 0.8196 0.28502 ...
    0.065469 0.0044517 0.018164 0.023305 0.02397 0.023141 0.021341 ...
    0.019364 0.017379 0.016061];
n = 48;

d = fdesign.arbmag('n,f,a',n,f,a);
hdc = design(d,'freqsamp','Window','rectwin');

[h,w] = freqz(hdc);
plot(w/pi,mag2db(abs(h)),f,mag2db(abs(a)),"--")

The plot shows the response for hdc from –1 to 1 in normalized frequency because the filter's transfer function is not symmetric around 0. Since the Fourier transform of the filter does not exhibit conjugate symmetry, design returns a complex-valued filter.

Version History

Introduced in R2009a