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