# Effect of FIR LPF coefficients decimation

I have a simple linear phase FIR LPF designed by windowing using

hamming window, obtained its mathematical expression (lets call it h[n]).

Now, decimating the sequency of the coefficients by 2, i.e. making new

filter to be h'[n] = h[2n] (an new n sequence runs from 0 to original

n/2, so if original LPF length is 51 (order 50), the new will run from

0 to 25)) and checking its impulse and frequency response in MATLAB I

see that it produces an equal -6dB magnitude at all frequencies

(making it all-pass filter with 1/2 magnitude), phase remains linear.

The impulse response of the new filter is all zeros except of the

middle coefficient which is maximum peak (0.5 in mag). This impulse

response looks as expected comparative to the one by the original LPF,

but how its frequency response can be proved mathematically ?

I guess I shall take its h[2n] expression and do DFT on one to obtain

it frequency response (so that taking the original h[n], substituting

into it 2n instead of n and then proceed with DFT on the obtained

expression).

Am I wrong ?

question is what is the frequency response of a decimated FIR linear

phase filter, then here is an explanation:

You can think of the filter coefficients as a discrete time signal and

the effect of decimation will be same as you observe on a signal. Let us

say original filter has a sampling rate Fs with cutoff Fc. So frequency

response will be flat till Fc and will roll off at a rate till Fs/2. So

decimating the coefficients will cause aliasing of the response from

Fs/4 to Fs/2 to 0 to Fs/4. Note new sampling rate will be Fs/2. So there

will be no change in the cutoff frequency but the response will change

slightly.

Regards,

Amit

________________________________

From: m... [mailto:m...] On Behalf

Of alexzfoto

Sent: Thursday, June 22, 2006 6:50 PM

To: m...

Subject: [matlab] Effect of FIR LPF coefficients decimation

Hi, here is the quesiton:

I have a simple linear phase FIR LPF designed by windowing using

hamming window, obtained its mathematical expression (lets call it

h[n]).

Now, decimating the sequency of the coefficients by 2, i.e. making new

filter to be h'[n] = h[2n] (an new n sequence runs from 0 to original

n/2, so if original LPF length is 51 (order 50), the new will run from

0 to 25)) and checking its impulse and frequency response in MATLAB I

see that it produces an equal -6dB magnitude at all frequencies

(making it all-pass filter with 1/2 magnitude), phase remains linear.

The impulse response of the new filter is all zeros except of the

middle coefficient which is maximum peak (0.5 in mag). This impulse

response looks as expected comparative to the one by the original LPF,

but how its frequency response can be proved mathematically ?

I guess I shall take its h[2n] expression and do DFT on one to obtain

it frequency response (so that taking the original h[n], substituting

into it 2n instead of n and then proceed with DFT on the obtained

expression).

Am I wrong ?

I have been read in some papers about that

"classical techniques suc as least-squared error

minmisation or Winer filtering would fail to deal with

real signal, because they were originally designed to

work with signals that have a Gaussian kernel"

and finally

"These classical techniques are usually PHASE-BLIND"

I can understood about the phase-blind, can any one

have introduction work about phase-blind related to

real signal(foer example:biomedical signal) ?

Thanks a lot,

Best Regards

Carlos Estombelo Montesco

+---------------------------+

| Carlos Alberto Estombelo Montesco |

| PhD. Student in Physics Applied to Medicine and Biology |

| Department of Physics and Mathematics |

| University of S Paulo (USP) |

| email: e...@gmail.com |

+---------------------------+