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Magnitude and Phase of Frequency Response

Module by: Richard Baraniuk. E-mail the author

Summary: An overview of the concepts behind the magnitude and phase of frequency response of LSI systems.

Y⁢k=H⁢k⁢X⁢k Y k H k X k (1)

where 0≤k≤N−1 0 k N 1 ,

H⁢k=|H⁢k|⁢ei⁢ ∡ ⁢H⁢k H k H k ∡ H k ,

and X⁢k=|X⁢k|⁢ei⁢ ∡ ⁢X⁢k X k X k ∡ X k .

ie:

|Y⁢k|⁢ei⁢ ∡ ⁢Y⁢k=(|H⁢k|⁢ei⁢ ∡ ⁢H⁢k)⁢(|X⁢k|⁢ei⁢ ∡ ⁢X⁢k) Y k ∡ Y k H k ∡ H k X k ∡ X k (2)
|Y⁢k|=|H⁢k|⁢|X⁢k| Y k H k X k (3)
ie: magnitude multiply
∡ ⁢Y⁢k= ∡ ⁢H⁢k+ ∡ ⁢X⁢k ∡ Y k ∡ H k ∡ X k (4)
ie: phases add so convolution of x x by h h changes magnitude and phase of x x's DFT coeffients.

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