2 Discrete-Time fourier Transform
2 Discrete-Time Fourier Transform
Introduce o The signals and systems can be analyzed in time-domain or frequency-domain o In time-domain, any arbitrary sequence can be represented as a weighted linear combination of delayed unit sample sequence, then the input-output relationship of LTI system can be obtained o The frequency-domain representation of a discrete-time sequence is also discussed in this chapter
Introduce ⚫ The signals and systems can be analyzed in time-domain or frequency-domain. ⚫ In time-domain, any arbitrary sequence can be represented as a weighted linear combination of delayed unit sample sequence, then the input-output relationship of LTI system can be obtained. ⚫ The frequency-domain representation of a discrete-time sequence is also discussed in this chapter
Introduce o In many applications, it is convenient to consider an alternate description of a sequence in terms of complex exponential sequences. This leads to a particularly useful representation of discrete-time sequences and certain discrete-time systems in frequency domain
Introduce ⚫ In many applications, it is convenient to consider an alternate description of a sequence in terms of complex exponential sequences. This leads to a particularly useful representation of discrete-time sequences and certain discrete-time systems in frequency domain
2.1 The Continuous-Time Fourier Transform We begin with a brief review of the continuous-time Fourier transform, a frequency-domain representation of a continuous-time signal, and its properties, as it will provide a better understanding of the frequency-domain representation of the discrete-time signals and systems in addition to pointing out the major differences between these two transform
2.1 The Continuous-Time Fourier Transform We begin with a brief review of the continuous-time Fourier transform, a frequency-domain representation of a continuous-time signal, and its properties, as it will provide a better understanding of the frequency-domain representation of the discrete-time signals and systems, in addition to pointing out the major differences between these two transform
2.1 The continuous-Time fourier transform e Definition of continuous-time ft Continuous-time Fourier transform(CTFT) xa(jQ)=xa( e-c Inverse continuous-time Fourier transform(ICTFT) X(iQe/ds 2丌
2.1 The Continuous-Time Fourier Transform • Definition of continuous-time FT ( ) ( ) j t X j x t e dt a a − − = ( ) ( ) 1 2 j t a a x t X j e d − = Continuous-time Fourier transform (CTFT) Inverse continuous-time Fourier transform (ICTFT)