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Magnitude and Phase of Frequency Response

Module by: Richard Baraniuk

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

Yk=HkXk Y k H k X k (1)

where 0≤k≤N-1 0 k N 1 ,

Hk=|Hk|ⅇⅈ∡Hk H k H k ∡ H k ,

and Xk=|Xk|ⅇⅈ∡Xk X k X k ∡ X k .

ie:

|Yk|ⅇⅈ∡Yk=|Hk|ⅇⅈ∡Hk|Xk|ⅇⅈ∡Xk Y k ∡ Y k H k ∡ H k X k ∡ X k (2)
|Yk|=|Hk||Xk| Y k H k X k (3)
ie: magnitude multiply
∡Yk=∡Hk+∡Xk ∡ 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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