Lecture 5 Problems 1． For the given system 0 :[ ] [ ] n D → → → ¡ ¡ Z Z , when the input is x(n) , the output y(n)=x(n-n 0 ). (1) Is system D n0 LTI? (2) Find H(ω). 2. A particular lecture hall produces linear, time-invariant acoustic distortion, which can be modeled reasonably well by a DT-LTI system F whose input denotes the sound of the speaker’s voice whose output y represents the speaker’s sound as perceived by a listener. In our simple model, what a listener hears is the superposition of two component signals: one component is the sound of the speaker’s voice arriving via direct path, without distortion or delay; the second components is the sound of the speaker’s voice arriving via indirect path as a reflection from a wall, ceiling or floor, and suffering from attenuation and delay. The impulse response of a system F that model the situation described above is characterized by: 1 ( ) ( ) ( 2) 2 f n n n δ δ = + - (a) Determine a reasonably simple expression for F(ω) , the frequency response of the acoustic model of the lecture hall environment. Also provide a well labeled sketch of the magnitude response |
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- Spring '14
- Vector Space, LTI system theory, representative, reasonably simple expression