fir filters (finite impulse response filters) · filter (fir coeff, 1, s3), %analfzar la serial...

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FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS)

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Page 1: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS)

Page 2: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

The General FIR Filter

The general form for the FIR filter is:

Page 3: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

MOVING AVERAGE FILTER

Page 4: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Moving average filter

Page 5: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Noise reductions vs. step response

Page 6: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Frequency response

Moving average is an exceptionally good smoothingf ilter (the action in

the time domain), but an exceptionally bad low-pass filter (the action in

the frequency domain).

Page 7: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Matlab

The filter …

Page 8: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 9: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Práctica

Page 10: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

WINDOWED-SINC FILTERS

Page 11: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Windowed-sinc filters are used to separate one band of frequencies from another. They are very stable and have exceptional frequency domain characteristics are obtained at the expense of poor performance in the time domain, including excessive ripple and overshoot in the step response. When carried out by standard convolution, windowed-sinc filters are easy to program, but slow to execute.

Page 12: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

sinc function

Page 13: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 14: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 15: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Hamming and Blackman window

Page 16: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 17: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Designing the Filter (fc and M)

Page 18: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Exercise

Page 19: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 20: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 21: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 22: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 23: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 24: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Page 25: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Exercise

Now eliminate the 1000 Hz frequency!!!

Page 26: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Example of Windowed-Sinc Filters,

electroencephalogram

Page 27: FIR FILTERS (FINITE IMPULSE RESPONSE FILTERS) · filter (fir coeff, 1, s3), %analfzar la serial filtrada y su fir coeff fir coeff Columns 1 through 1 espectra de frecuencfas o 20

Example of Windowed-Sinc Filters,

band-passfilter

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