Signals and Systems - Electrical Engineering

584 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems with the wholez-plane (except for the origin) as its ...

10.2 Discrete-Time Fourier Transform 585 FIGURE 10.3 Top: Downsampler and decimator. Bottom: upsampler and interpolator. H(z) H( ...

586 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems (a) (b) 0 5 10 15 0 5 10 15 0 5 10 15 0 0.5 1 x[ n] ...

10.2 Discrete-Time Fourier Transform 587 (a) (b) 024681012141618 −0.4 −0.2 0 s[ n]− x[ n] 0 2 4 6 8 10 12 14 16 18 0 0.2 0.4 0.6 ...

588 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems In a dual way, when we multiply a signal by a comple ...

10.2 Discrete-Time Fourier Transform 589 =π [ δ(ω−ω 0 )e−jπ/^2 +δ(ω+ω 0 )ejπ/^2 ] =−jπ[δ(ω−ω 0 )−δ(ω+ω 0 )] Thus, the frequency ...

590 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems nExample 10.8 For the signalx[n]=αnu[n], 0< α < ...

10.2 Discrete-Time Fourier Transform 591 In particular, ifφ=0, the signalx[n] is a cosine and its phase is zero. Ifφ=−π/2,x[n] i ...

592 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems Phase unwrapping Another problem with phase computat ...

10.2 Discrete-Time Fourier Transform 593 FIGURE 10.6 Phase spectrum of sinusoid in Gaussian noise using magnitude masking: (a) m ...

594 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems linear and continuous. Indeed, the transfer function ...

10.2 Discrete-Time Fourier Transform 595 H1up = unwrap(H1p); % unwrapped phase of H1(z) H2m = abs(H2(1:128)); H2p = angle(H2(1:1 ...

596 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems Solution Notice that if 1/αiis a zero ofHi(z), a pol ...

10.3 Fourier Series of Discrete-Time Periodic Signals 597 representation for discrete-time periodic signals that is discrete and ...

598 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems ofkinto an infinite number of finite segments of len ...

10.3 Fourier Series of Discrete-Time Periodic Signals 599 x[0], x[4],... x[1], x[5],... x[2], x[6],... x[3], x[7],... ··· ··· n ...

600 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems The Fourier series representation of a periodic sign ...

10.3 Fourier Series of Discrete-Time Periodic Signals 601 Solution The period ofx[n] isN=4. Indeed, x[n+4]= 1 +cos( 2 π(n+ 4 )/ ...

602 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems Solution The Fourier series coefficients are found a ...

10.3 Fourier Series of Discrete-Time Periodic Signals 603 Solution The DTFT ofδM[n] is given by (^1) M(ejω)= ∑∞ m=−∞ F(δ[n−mM])= ...