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BIEN425 – Lecture 10
•By the end of the lecture, you should be able to:
–Describe the reason and remedy of DFT leakage
–Design and implement FIR filters using rectangular,
Hanning, Hamming and Blackman windowing methods
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DSP lecture hamming window, Lecture notes of Electronic Technology
digital signal processing hamming lecture
Typology: Lecture notes
2018/2019
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BIEN425 – Lecture 10
- (^) By the end of the lecture, you should be able to:
- (^) Describe the reason and remedy of DFT leakage
- (^) Design and implement FIR filters using rectangular, Hanning, Hamming and Blackman windowing methods
DFT leakage
- (^) Leakage occurs because the DFT X(i) produces accurate results only when input data has energy precisely at discrete analysis frequencies given by ifs/ N.
- (^) What happens if input signal has component at intermediate frequencies?
- (^) This is due to correlation between two waves, one of which does not have an integral number of cycles in N points; therefore the sum for the correlation computation is not zero.
Why rectangular windows?
Spectrum of rectangular
window
- (^) For N points and window (unit value) length of K, we can obtain the frequency spectrum which takes the form of Dirichlet Kernel (Lecture10.m) First zero of the mainlobe occurs at n = N/K. Mainlobe
Some windows
- (^) Filter transfer function can be re-written as:
- (^) First we determine h(i) based on our filter specs, then we decide the windows w(i)
- (^) Similarly for Type 3 and 4 linear phase filters:
- To find h(i), simply insert the right form of Ar(f) based on the filter characteristics into the correct equation.
- (^) In general, for Type 1 linear-phase filter with order m=2p, h(k) can be written as follows
General strategy (ideal)
- (^) Pick m
- (^) Pick a window w(i)
- (^) Pick a Type 1 ideal impulse response h(i) from Table 6.
- (^) Compute bi = w(i)h(i)
• Compute H(z)
m i i i H z bz 0
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Example
-120 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.
- 0 20 Lowpass filter using Hanning window f/fs A(f) (dB) -120 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.
0 20 Lowpass filter using Blackman window f/fs A(f) (dB)
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General strategy (non-ideal)
- (^) Pick m
- (^) Pick a window w(i)
- (^) Pick Ar(f)
- Compute bi = w(i)h(i) based on your filter type (1-4)
- (^) For Type 1 and 2
- (^) For Type 3 and 4
- (^) Compute H(z)
m i i i H z bz 0