In this method, we designed FIR Filter using frequency sampling method.Unlike the window method, this technique can be used for any given magnitude response.
Input Specifications given were:
Thus, sampling the continuous frequency response Hd(w) at N points essentially gives us the N-point DFT of Hd(2(pi)kn/N).
By using the IDFT formula, the filter co-efficients are calculated. Now using the above N-point filter response, the continuous frequency response is calculated as an interpolation of the sampled frequency response. The approximation error would then be exactly zero at the sampling frequencies and would be finite in frequencies between them. The smoother the frequency response being approximated, the smaller will be the error of interpolation between the sample points.
Input Specifications given were:
1) Pass band attenuation
2) Stop band attenuation
3) Pass band frequency
4) Stop band frequency
5) Sampling frequency
Frequency response is calculated using input specification.Now this frequency response is sampled at a set of equally spaced
frequencies to obtain N samples. 2) Stop band attenuation
3) Pass band frequency
4) Stop band frequency
5) Sampling frequency
Thus, sampling the continuous frequency response Hd(w) at N points essentially gives us the N-point DFT of Hd(2(pi)kn/N).
By using the IDFT formula, the filter co-efficients are calculated. Now using the above N-point filter response, the continuous frequency response is calculated as an interpolation of the sampled frequency response. The approximation error would then be exactly zero at the sampling frequencies and would be finite in frequencies between them. The smoother the frequency response being approximated, the smaller will be the error of interpolation between the sample points.
Frequency Sampling realization is computationally more efficient.
ReplyDeleteThis is because it leads to fewer coefficients
DeleteFSM is used where desired response is already known.
ReplyDeleteYes
DeleteDiscontinuity is observed in phase plot between lobes and also when the phase spectrum goes out of the range of -pi to pi.
ReplyDeleteWhat was the sampling frequency used?
ReplyDeleteHowever, FSM causes time-aliased output
ReplyDeleteYes
DeleteComputational efficiency is increased as signal is decomposed which makes calculation faster
ReplyDelete