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DECEMBER 4, 1996 EE 4773/6773: LECTURE NO. 46 PAGE 1 of 2
ELECTRICAL AND COMPUTER ENGINEERING
v n( )
Multirate Signal Processing: Signal Interpolation
How do we change the sample frequency of a signal:
Method 1: Use the sampling theorem (Lecture No. 3)
Define as the original sample frequency, and as the new
sample frequency. Recall our interpolation function, where :
may be expressed as:
What are the disadvantages of this method? Method 2:
Consider the signal. What is the spectrum of?
F (^) s^1 F (^) s^2
B
F (^) s^1 2
g t( ) sin(^2 πBt) 2 πBt
x m F (^) s^2
x m F (^) s
(----- 2 - ) x n F (^) s
(----- 1 - )g m F (^) s
n F (^) s
n =–∞
∞
x n( ) v n( ) = x Ln( )
Recall the frequency-scaling property:
V (ω ) v m( )e –^ jωm m =–∞
∞
v n( )e –^ jωnL n =–∞
∞
= X (ω L)
DECEMBER 4, 1996 EE 4773/6773: LECTURE NO. 46 PAGE 2 of 2
ELECTRICAL AND COMPUTER ENGINEERING
Signal Interpolation/Decimation By A Ratio Of Integers
F (^) s new( ) F (^) s old( )^ U D
Note that the LPF is run at the decimation rate of D!
Questions:
- Under what conditions will this introduce no distortion?
- How do we implement this efficiently?
- How should we convert from 8 kHz to 6.4 kHz?
- What about the infamous 44.1 kHz CD sample frequency?
Zero-Stuff: U-1 zeros
Decimate By D Samples
LPF
F (^) s(old)
x(n)
Fs(old)
y(n)
Fs(new)
v(n) (^) z(n)
V(f)
f f s old( ) f^ s old( )U
new sample frequency
Z(f)
f f s old( ) f^ s old( )U
Y(f)
f f s old( ) f^ s old( )U D
X(f)
f f s old( )
