S t l A l i ith th DFTSpectral Analysis with the DFT
1DSP, Lecture 14
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The Effect of WindowingThe Effect of Windowing
Consider a continuous signal of sum of two sinusoidal signals:Consider a continuous signal of sum of two sinusoidal signals:
After Sampling with on aliasing:
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Specially, we can rewrite it as:Specially, we can rewrite it as:
Example: pf = 100 kHzθ0 =θ1=0The Length of w[n] = 64A0=1, A1= 0.75
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• Reduced resolution and leakage areReduced resolution and leakage are two primary effects on the spectrum
l f l i i d has a result of applying a window to the signal. g
• The resolution is influenced by the id h f i l b fW(j )width of main‐lobe of W(jω)
• The degree of leakage depends on theThe degree of leakage depends on the amplitude of side‐lobes, respect to the
li d f i l bamplitude of main‐lobe DSP, Lecture 14 12
Design using Kaiser WindowDesign using Kaiser Window• Assume:• Δml = Width of Main‐Lobe • And Asl = the ratio of Main‐lobe to the
Largest side‐Lobe (in dB)
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The effect of spectral SamplingThe effect of spectral Sampling
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The previous example, but with N=128, (Zero padding)
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The effect of windowThe effect of window
• Assuming Kaiser WindowAssuming Kaiser Window
We assume that:β= 5.48 and L=64
Then we will have:A l = 40 dB and Δ l = 0 401Asl = ‐40 dB and Δml = 0.401
Not that:
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Which is very close to Δml ( Design procedure is reverse!)
Magnitude of DFT for N=L=64
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DFT for N=L=32
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L= 32 But N=64
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L=32 and N=1024
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