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2004
In this chapter, the discrete Fourier transform (DFT) will be discussed. The Fourier transform discussed in the previous chapter is quite useful, but the applications will be limited for two reasons. First, the function in the time domain must be representable in closed form so that the Fourier integral can be performed. Thus, unless the input function
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In this chapter, the discrete Fourier transform (DFT) will be discussed. The Fourier transform discussed in the previous chapter is quite useful, but the applications will be limited for two reasons. First, the function in the time domain must be representable in closed form so that the Fourier integral can be performed. Thus, unless the input function
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Discrete-Time Fourier Transform Discrete Fourier Transform
2022Muhammad N. Khan +2 more
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1996
In Section 2.3 of Chapter 2, the notion of an integral transform was introduced in a general way. The emphasis there was on the use of such transforms, like the Laplace and Fourier transforms, in reducing differential operators to algebraic operators, hence the “operational calculus” method of solving differential equations. A special case in which the
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In Section 2.3 of Chapter 2, the notion of an integral transform was introduced in a general way. The emphasis there was on the use of such transforms, like the Laplace and Fourier transforms, in reducing differential operators to algebraic operators, hence the “operational calculus” method of solving differential equations. A special case in which the
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2017
In linear algebra, basis vectors span the entire vector space. And any vector of the vector space can be written as the linear combination of the basis vectors. For any vector in vector space, finding the coefficients of basis vectors used for the construction of the vector can be considered as a transformation.
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In linear algebra, basis vectors span the entire vector space. And any vector of the vector space can be written as the linear combination of the basis vectors. For any vector in vector space, finding the coefficients of basis vectors used for the construction of the vector can be considered as a transformation.
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1989
In chapter 6, we investigated the definition and properties of the discrete-time Fourier transform X(e jω ), with ω being a continuous frequency variable, and found it to be very useful for analyzing a wide variety of signals and systems of theoretical interest.
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In chapter 6, we investigated the definition and properties of the discrete-time Fourier transform X(e jω ), with ω being a continuous frequency variable, and found it to be very useful for analyzing a wide variety of signals and systems of theoretical interest.
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