DSP FIRST 2e  Examples 93


A.1: Polar to Rectangular

  • –1
 

A.2: Euler’s Formula

  • –2
 

A.3: Degrees to Radians

  • –3
 

A.4: Adding Polar Forms

  • –4
 

A.5: 7th Roots of Unity

  • –5
 

C.1: Square Wave

  • –6
 

C.2: New Square Wave

  • –7
 

C.3: Time-Scaling Pulse Waves

  • –8
 

C.4: Delayed Triangular Wave

  • –9
 

C.5: Differentiated Triangular Wave

  • –10
 

C.6: Average Power of a Sinusoid

  • –11
 

2.1: Plotting Sinusoids

  • –12
 

3.1: Two-Sided Spectrum

  • –13
 

3.10: Average Power in Sinusoid

  • –14
 

3.11: Average Power in Square Wave

  • –15
 

3.12: Synthesize a Chirp Formula

  • –16
 

3.2: Adding Spectra

  • –17
 

3.3: Delayed Cosine

  • –18
 

3.4: Derivative of Sine plus DC

  • –19
 

3.5: Spectrum of a Product Signal

  • –20
 

3.6: Decreasing the Frequency Difference, \(f_\Delta\)

  • –21
 

3.7: Amplitude Modulation

  • –22
 

3.8: Fundamental Period T0

  • –23
 

3.9: Calculating F0

  • –24
 

5.1: Pulse Input to 3-Point Running Average

  • –25
 

5.2: FIR Filter Coefficients

  • –26
 

5.3: Pulse as the Difference of Two Shifted Unit Steps

  • –27
 

5.4: Impulse Response of Cascaded Systems

  • –28
 

6.1: Formula for the Frequency Response

  • –29
 

6.10: Frequency Responses in Cascade

  • –30
 

6.11: Cascade

  • –31
 

6.12: Cascade

  • –32
 

6.13: Time Delay of FIR Filter

  • –33
 

6.2: Complex Exponential Input

  • –34
 

6.3: Cosine Input

  • –35
 

6.4: Three Sinusoidal Inputs

  • –36
 

6.5: Steady-State Output

  • –37
 

6.6: \(h[n]\) ←→ \(H(e^{j\hat\omega})\)

  • –38
 

6.7: Difference Equation from \(H(e^{j\hat\omega})\)

  • –39
 

6.8: First-Difference Removes DC

  • –40
 

6.9: Lowpass Filter

  • –41
 

7.1: DTFT of an FIR Filter

  • –42
 

7.2: DTFT of a Complex Exponential?

  • –43
 

7.3: Delayed Sinc Function

  • –44
 

7.4: Frequency Response of Delay

  • –45
 

7.5: Energy of the Sinc Signal

  • –46
 

7.6: Ideal Lowpass Filtering

  • –47
 

7.7: Transition Width versus Filter Order

  • –48
 

8.1: Short-Length DFT

  • –49
 

8.10: Period of a Discrete-Time Sinusoid

  • –50
 

8.11: Fourier Series of a Sampled Signal

  • –51
 

8.12: Sum of Two Sinusoids

  • –52
 

8.2: Short-Length IDFT

  • –53
 

8.3: DFT Symmetry

  • –54
 

8.4: Frequency Response Plotting with DFT

  • –55
 

8.5: DFT of Shifted Impulse

  • –56
 

8.6: Modulo- N Arithmetic

  • –57
 

8.7: Convolution of Pulses

  • –58
 

8.8: Synthesize a Periodic Signal from DFS

  • –59
 

8.9: Conjugate Symmetry of DFS Coefficients

  • –60
 

9.1: \(z\mbox{-}\)Transform of a Signal

  • –61
 

9.10: Nulling Signals with Zeros

  • –62
 

9.11: \(H(e^{j\hat\omega})\) from \(H(z)\)

  • –63
 

9.2: Inverse \(z\mbox{-}\)Transform

  • –64
 

9.3: Zeros of System Function

  • –65
 

9.4: Difference Equation from Roots of \(H(z)\)

  • –66
 

9.5: Convolution via \(H(z)\)X (z)

  • –67
 

9.5a:

  • –68
 

9.6: \(H(z)\) for Cascade

  • –69
 

9.7: Split \(H(z)\) into a Cascade

  • –70
 

9.8: Deconvolution

  • –71
 

9.9: Moving from \(\hat\omega\)

  • –72
 

10.1: IIR Block Diagram

  • –73
 

10.10: Plot \(H(e^{j\hat\omega})\) via MATLAB

  • –74
 

10.10a:

  • –75
 

10.11: Inverse \(z\mbox{-}\)Transform

  • –76
 

10.12: Long Division and Partial Fractions

  • –77
 

10.13: Transient and Steady-State Responses

  • –78
 

10.14: Complex Poles

  • –79
 

10.15: Second-Order System Real Poles

  • –80
 

10.16: Second-Order System

  • –81
 

10.17: Poles on Unit Circle

  • –82
 

10.18: Stable Complex Poles

  • –83
 

10.19: Frequency Response of a Second-Order System

  • –84
 

10.2: Impulse Response

  • –85
 

10.20: MATLAB for \(H(e^{j\hat\omega})\)

  • –86
 

10.3: IIR Response to General Input

  • –87
 

10.4: Unstable System

  • –88
 

10.5: MATLAB for IIR Filter

  • –89
 

10.6: \(H(z)\) from Impulse Response

  • –90
 

10.7: Find Poles and Zeros

  • –91
 

10.8: Zeros at \(z=\infty\)

  • –92
 

10.9: Stability from Pole Location

  • –93