Digital Filters,Demodulation

Nov. 16, 21

11/16/2006 YGK, Phys250

FIR filters

11/16/2006 YGK, Phys250

Box-car Filter Response

11/16/2006 YGK, Phys250

Time-Domain Signal After Filteringfsignal=fs/32

fsignal=3fs/32

11/16/2006 YGK, Phys250

Frequency-Domain Response

11/16/2006 YGK, Phys250

More FIR Filters

5-tap “Gaussian” FIR filter

11/16/2006 YGK, Phys250

Ideal Low-Pass FIR FilterFrequency response

Time-domain coefficients

11/16/2006 YGK, Phys250

Convoluted Low-Pass Filter

11/16/2006 YGK, Phys250

Example: Blackman Window(approximates Gauss)

Magnitude of time-domain response

dB

11/16/2006 YGK, Phys250

More (Tunable) Filters

(c.f. hardware filters)

11/16/2006 YGK, Phys250

More Tunable Filters

11/16/2006 YGK, Phys250

Bandpass Filter

11/16/2006 YGK, Phys250

Highpass Filter

11/16/2006 YGK, Phys250

Phase Response in FIR FiltersLinear phase shift in passband: constant group delay (no spectral distortions): good !

11/16/2006 YGK, Phys250

IIR Filters

11/16/2006 YGK, Phys250

Example: Exponential AveragingFilter

y(n)=αx(n)+(1-α)x(n-1)

11/16/2006 YGK, Phys250

Exponential IIR Filter

11/16/2006 YGK, Phys250

Hilbert Transform

: H(ω)=j, ω≥0; H(ω)=-j, ω<0

90o phase shift:

11/16/2006 YGK, Phys250

Hilbert Transform Applications

AM Demodulation

Standard mixing

Amplitude after HT

11/16/2006 YGK, Phys250

HT ApplicationsFrequency translation

Standard mixing

HT with complex multiplication

11/16/2006 YGK, Phys250

Discrete HT

11/16/2006 YGK, Phys250

Time-Domain HT

FIR filter implementation:

11/16/2006 YGK, Phys250

Time-Domain HT

15-tap HT

11/16/2006 YGK, Phys250

Time-Domain HTPhase-shift compensated