# concise dsp tutorial by BEERNARD KLAR

By BEERNARD KLAR

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1 0 1 1 2 3 4 time, k The impulse response of a simple 5 weight linear phase FIR filter and the corresponding z-domain plane plot. 3 0 1 Real -1 -2 Minimum/Maximum Phase If the zeroes of an FIR filter all lie within the unit circle on the z-domain plane, then the filter is said to be minimum phase. If the zeroes all lie outside then the filter is maximum phase. If there are zeroes both inside and outside the filter then the filter is non-minimum phase. e. all of the poles lie within the unit circle.

22140... 25669... (Truncated to 5 decimal places) 15 The impulse response h ( k ) = w k of a low pass filter, FIR1 with 15 weights, a sampling rate of 10000 Hz, and cut off frequency designed at around 1000Hz. the Companion CD DIGITAL COMMUNICATIONS BERNARD SKLAR 2nd Edition 38 Concise DSP Tutorial - Robert W. 2 0 1000 2000 3000 4000 -10 -20 -30 -40 5000 20 log H ( f ) frequency (Hz) Linear Magnitude Response 0 1000 2000 3000 4000 5000 frequency (Hz) Logarithmic Magnitude Response The 1024 point FFT (zero padded) of the above low pass filter impulse response, FIR1.

The last N input samples are weighted by the filter coefficients to produce the output y ( k ) The general output equation (convolution) for an FIR filter is: y ( k ) = w 0 x ( k ) + w1 x ( k – 1 ) + w 2 x ( k – 2 ) + w 3 x ( k – 3 ) + ..... + w N – 1 x ( k – N + 1 ) N–1 = (63) ∑ wn x ( k – n ) n=0 The term finite impulse response refers to the fact that the impulse response results in energy at only a finite number of samples after which the output is zero. e. the output will decay to zero within a finite time.