Bode Plots 28 Mar 19 EIE3001 Sig Sys Spring 2019 13 1 Try to verify that the

# Bode plots 28 mar 19 eie3001 sig sys spring 2019 13 1

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Bode Plots 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 13 1. Try to verify that the slope is -20 dB per decade 2. If we design two RC circuits, -40 dB per decade can be achieved asymptotically (more complicated to analyze though)

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Discrete-time Filter Examples ¾ Non-recursive (moving average) filters 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 14 Input signal weights Output signal h[n] 5-point average with equal weights H(Omega) In these examples, the filters are non-causal Question: How to sketch the impulse response from the moving average formula?
Discrete-time Filter Examples ¾ Recursive filters 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 15 We have analyzed a first-order example: Recursive: current output depends on the past output

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Impulse Response and Frequency Response of Recursive Filters 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 16
A Short Summary ¾ We studied the characteristics of Ideal filters RC circuit as an example of continuous-time filter Discrete-time non-recursive and recursive filters ¾ The goal of this lecture is to understand the basic concept of filtering Many systems can be described as an LTI system. If it can be modeled into an LTI system, the concept of impulse response and frequency response can be applied to analyze the system Understand the design tradeoffs Mathematical tool for interpretation: convolution property of Fourier transform 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 17

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Amplitude Modulation 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 18 ¾ Three parameters to modify a sinusoidal signal Amplitude, frequency, and phase ¾ Amplitude modulation
Why Modulation ¾ For easy to transmit through the medium Electromagnetic wave is easier to generate at not-so-low frequency To transit signal at a dedicated frequency band (depending on application, technology, regulation, etc.) ¾ Multiplexing, and more… More bandwidth to carry information at a higher carrier frequency Transmit different signals simultaneously (frequency division multiplexing, FDM) Filter design 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 19

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Complex Exponential Carrier 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 20 As we will see later, knowing the phase of the carrier signal is important for demodulation, and that is why we explicitly express it in the notation.
Spectrum of the Modulation Step 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 21

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Demodulation Step 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 22
Implementation using Only Real Signals 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 23

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Design a Bandpass Filter using Exponential Carrier Modulation 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 24 passband ¾ We wish to extract only the portion of the signal fallen within the red window (in frequency domain) ¾ Challenge: Sometimes difficult to design bandpass filter given arbitrary specification Could be difficult to adjust the filter if we change the filter requirement It is often easier to build a fixed filter (fixed center frequency, passband, etc.)
Design a Bandpass Filter using Exponential Carrier Modulation 28-Mar-19 EIE3001 Sig & Sys, Spring 2019 25 passband

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