Digital Signal Processing Lecture 4 DTFT add slide for format types , d , f, c etc Dr. Shoab Khan

Complex Exp Input Signal

The Frequency Response

Delay and First Difference

More on the Ideal Delay

Discrete Time Fourier Transform

Fourier with DTFT Mag-Phase

Properties

Properties…(cont)

Symmetric Properties DTFT Properties:

Consequences of Hermitian Symmetry If then And symmetry

DTFT- Sinusoids

DTFT of Unit Impulse

Ideal Lowpass Filter

Example

Magnitude and Angle Form

Magnitude and Angle Plot

Example

Real and Even ( Zero Phase) Consider an LTI system with an even unit sample response DTFT is = e 2 j w + 3 - cos( ) 4

Real & Even (Zero Phase) Frequency response is real, so system has “zero” phase shift This is to be expected since unit sample response is real and even.

Linear Phase symmetryLP

Useful DTFT Pairs

Convolution Theorem

Linear Phase… ( cont.)

freqfilter

Frequency Response of DE

Matlab

Example

Ideal Filters

Ideal Filters

Ideal Lowpass Filter

h[n] of ideal filter

Approximations

Freq Axis

Inverse System