文档介绍：Chapter 3 Discrete-Time Fourier Transform
The Definition
The Theorems
The Frequency Response of an LTI DTS
Phase and Group Delays
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How to Represent the Discrete-Time Signal?
Time-domain(a weighted bination of delayed unit sample sequences.)
Transform-domain a. frequency domain b. Z domain (a sequence in terms plex exponential sequences of the form{ } and { }.
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Several Forms of FT
FT-continuous in time,continuous in frequency
x(t)
t
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Result:
Continuous function in time domain will cause non-periodicity in frequency domain,whereas the non-periodicity in time domain will cause Continuous function in frequency domain.
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FS-continuous in time,discrete in frequency
x(t)
T0
Where:
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Result:
Continuous function in time domain will cause non-periodicity in frequency domain,whereas the periodicity in time domain will cause discrete frequency spectrum.
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The Continuous-Time Fourier Transform
It’s an useful tool to represent a continuous-time signal in frequency-domain.
It briefly called CTFT.
The relationship between it’s time and frequency is: continuous and non-periodic in time-domain, continuous and non-periodic in frequency-domain.
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The Definition
The definition of CTFT is:
The CTFT often is referred to as the Fourier spectrum.
The I-CTFT(inverse CTFT) is:
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We denote the CTFT pair of above two equations as:
The CTFT is plex function of in the range . It can be expressed in polar form as
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Energy Density Spectrum
Based on Parseval’s relation:
The total energy of a finite-energy continuous-plex signal is given by:
So we get energy density spectrum of is:
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