DSP lecture hamming window, Lecture notes of Electronic Technology

digital signal processing hamming lecture

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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
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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