Signals and systems Fall 2003 Lecture #7 25 September 2003 1. Fourier Series and lti Systems Frequency Response and Filtering 3. Examples and demos
Signals and Systems Fall 2003 Lecture #7 25 September 2003 1. Fourier Series and LTI Systems 2. Frequency Response and Filtering 3. Examples and Demos
The eigenfunction Property of Complex Exponentials CT st h(se CT System Function H()= h(tes dt DT h DT System Function" H(a)=2hinlz-n
The Eigenfunction Property of Complex Exponentials DT: CT: CT "System Function" DT "System Function
Fourier Series: Periodic Signals and lti systems r() ∑ t)=∑ Howo hoJkwot ak→→H(k0)ak gain So|ak一→|H(jko) H(kwo)=H(kwo)le ∠H(kuo) or powers of signals get modified through filter/system includes both amplitude phase ∑akck y=∑H(ck kwon hInI k=<N> k=<N> k kwak jk H ∠H ncludes both amplitude phase
Fourier Series: Periodic Signals and LTI Systems
The Frequency response of an LTI System Hu) H( l weSt CT Frequency response: H(jw)=/ h(t)e utat H JejuN DT Frequency response: H(ebu ∑ hne y
The Frequency Response of an LTI System CT notation
Frequency shaping and filtering By choice of HGo(or H(e/o) as a function of @ we can shape the frequency composition of the output Preferential amplification Selective filtering of some frequencies Example #1: Audio System Adjustable Filter equalizer er Bass. Mid-range, Treble controls For audio signals, the amplitude is much more important than the phase
Frequency Shaping and Filtering • By choice of H(j ω) (or H(ej ω)) as a function of ω, we can shape the frequency composition of the output - Preferential amplification - Selective filtering of some frequencies Example #1: Audio System Adjustable Filter Equalizer Speaker Bass, Mid-range, Treble controls For audio signals, the amplitude is much more important than the phase