chap4_lec2 - C hapte r4 Bandpass S ignalling Bandpass Filte...

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Eeng 360 1 Chapter4 Bandpass Signalling Bandpass Filtering and Linear Distortion Bandpass Sampling Theorem Bandpass Dimensionality Theorem Amplifiers and Nonlinear Distortion Total Harmonic Distortion (THD) Intermodulation Distortion (IMD) Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University
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Eeng 360 2 Bandpass Filtering and Linear Distortion Equivalent Low-pass filter: Modeling a bandpass filter by using an equivalent low pass filter (complex impulse response) ] ) ( Re[ ) ( 1 1 t jw c e t g t v = ] ) ( Re[ ) ( 2 2 t jw c e t g t v = ] ) ( Re[ ) ( 1 1 t jw c e t k t h = * 1 1 ( ) ( ) ( ) 2 2 c c H f K f f K f f = - + - ( 29 ( 29 [ ] c c f f G f f G f V - - + - = * 2 1 ) ( ( 29 { } t j c e t g t v ϖ ) ( Re = ) ( 1 t v ) ( 2 t v ) ( 1 t h ) ( f H Input bandpass waveform Output bandpass waveform Impulse response of the bandpass filter Frequency response of the bandpass filter H ( f ) = Y ( f )/ X ( f ) Bandpass filter
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Eeng 360 3 Bandpass Filtering
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Eeng 360 4 Bandpass Filtering ( 29 ( 29 ( 29 ; 2 1 2 1 2 1 1 2 t k t g t g = ( 29 ( 29 ( 29 f K f G f G 2 1 2 1 2 1 1 2 = ( 29 ( 29 ( 29 f H f V f V 1 2 = ( 29 ( 29 [ ] c c f f G f f G - - + - * 2 2 2 1 ( 29 ( 29 [ ] ( 29 ( 29 [ ] c c c c f f K f f K f f G f f G - - + - - - + - = * * 1 1 2 1 2 1 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 - - - - + - - - + - - - + - - = c c c c c c c c f f K f f G f f K f f G f f K f f G f f K f f G * * 1 * 1 * 1 1 4 1 ( 29 ( 29 , 0 * 1 = - - - c c f f K f f G Theorem: g (t) – complex envelope of input k(t) – complex envelope of impulse response Also, Proof: Spectrum of the output is Spectra of bandpass waveforms are related to that of their complex enveloped But ( 29 ( 29 . 0 * 1 = - - - c c f f K f f G ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 - - - - + - - = - - + - c c c c c c f f K f f G f f K f f G f f G f f G * * 1 1 * 2 2 2 1 2 1 2 1 2 1 2 1 2 1 The complex envelopes for the input, output, and impulse response of a bandpass filter are related by
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Eeng 360 5 Bandpass Filtering ( 29 ( 29 ( 29 f K f G f G 2 1 2 1 2 1 1 2 = Taking inverse fourier transform on both sides ( 29 ( 29 ( 29 ; 2 1 2 1 2 1 1 2 t k t g t g = Thus, we see that Any bandpass filter may be described and analyzed by using an equivalent low-pass filter.
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