# Shifting the Sinc filter in the frequency domain

Started by February 1, 2018
```Hello,

The following example from dsprelated.com shows the design of Sinc filter
with the following parameters.

The link of the example as below;
https://www.dsprelated.com/freebooks/sasp/Example_1_Low_Pass_Filtering.html

With the Matlab command fftshift the frequency response of the filter is
centered at 0 frequency which is 256 the frequency bin.

My question is, how can I move the center of this filter from the
frequency bin 256 to the frequency bin 150?

% Signal parameters:
f = [ 440 880 1000 2000 ];      % frequencies
M = 256;                        % signal length
Fs = 5000;                      % sampling rate

Filter parameters:
L = 257;    % filter length
fc = 600;   % cutoff frequency

% Design the filter using the window method:
hsupp = (-(L-1)/2:(L-1)/2);
hideal = (2*fc/Fs)*sinc(2*fc*hsupp/Fs);
h = hamming(L)' .* hideal; % h is our filter

% Choose the next power of 2 greater than L+M-1
Nfft = 2^(ceil(log2(L+M-1))); % or 2^nextpow2(L+M-1)

plot(abs(fftshift(fft(h,512))))

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```
```On 02/01/2018 09:24 AM, runinrainy wrote:
> Hello,
>
> The following example from dsprelated.com shows the design of Sinc filter
> with the following parameters.
>
> The link of the example as below;
> https://www.dsprelated.com/freebooks/sasp/Example_1_Low_Pass_Filtering.html
>
> With the Matlab command fftshift the frequency response of the filter is
> centered at 0 frequency which is 256 the frequency bin.
>
> My question is, how can I move the center of this filter from the
> frequency bin 256 to the frequency bin 150?
>

Translation in the frequency domain is multiplication by a sine wave
(for real, symmetric around DC translation) or by a complex exponential
(for complex, look Ma I've got twice as wide a datapath translation).

--
Rob Gaddi, Highland Technology -- www.highlandtechnology.com
Email address domain is currently out of order.  See above to fix.
```