Digital Signal Processing Here, without using Matlab\'s filter design functions,

Question

Digital Signal Processing

Here, without using Matlab's filter design functions, you will design your own filer by just placing poles and zeros visually. Perform the followings: (a) For a bandpass filter with cutoff frequencies of pi/4 and pi/2, place poles and zeros in the z-plane. You may use up to a total of 20 poles and zeros. Then plot the poles and zeros using Matlab's functions. (b) Determine H(e^j omega) and plot its magnitude in dB scale. (c) Then play with the locations and magnitude of the poles and zeros freely and observe how the magnitude of H(e^j omega) changes. You should at least find three scenarios on how to make H(e^j omega) a better bandpass filer. (d) Plot your final H(e^j omega)'s magnitude, the group delay, and the pole-zero diagram. (e) For the input signal x[n] = cos(pi/6n) + cos(pi/3n) (4) find the output and then observe that indeed the filter acts as a bandpass filter.

Explanation / Answer

Filter Design Using MATLAB

Digital filters are central to almost every signal processing system. Filters eliminate unwanted artifacts from signals to enhance their quality and prepare them for further processing. Digital filters are used in a variety of signal processing tasks including outlier and noise removal, waveform shaping, signal smoothing, and signal recovery.

MATLAB® and DSP System Toolbox provide extensive resources for filter design, analysis, and implementation. You can smooth a signal, remove outliers, or use interactive tools such as Filter Design and Analysis tool to design and analyze various FIR and IIR filters. You can also compare filters using the Filter Visualization tool and design and analyze analog filters using built in functions.

For implementing filters on embedded hardware, you can convert your filters to fixed point and analyze quantization effects using the DSP System Toolbox. You can also implement filters using structures like direct-form FIR, overlap-add FIR, direct-form II with second-order sections, cascade all-pass, and lattice structures. You can generate HDL code from filter designs for deployment onto FPGAs and ASICs.

SIGNAL AND SYSTEM ANALYSIS.
1. Signal Processing.
Motivation. Digital and Analog Processing. Total Harmonic Distortion (THD). A Notch Filter. Active Noise Control. Video Aliasing. Signals and Systems. Signal Classification. System Classification. Sampling of Continuous-time Signals. Sampling as Modulation. Aliasing. Reconstruction of Continuous-time Signals. Reconstruction Formula. Zero-order Hold. Delayed First-order Hold. Prefilters and Postfilters. Anti-aliasing Filter. Anti-imaging Filter. DAC and ADC Circuits. Digital-to-analog Conversion (DAC). Analog-to-digital Conversion (ADC). DSP Companion. Installation. Menu Options. GUI Modules. Functions. GUI Modules and Case Studies. Chapter Summary. Problems. Analysis. GUI Simulation. MATLAB® Computation.
2. Discrete-Time Systems in the Time Domain.
Motivation. Home Mortgage. Range Measurement with Radar. Discrete-time Signals. Signal Classification. Common Signals. Discrete-time Systems. Difference Equations. Zero-input response. Zero-state response. Block Diagrams. The Impulse Response. FIR Systems. IIR Systems. Convolution. Linear Convolution. Circular Convolution. Zero Padding. Deconvolution. Polynomial Arithmetic. Correlation. Linear Cross-correlation. Circular Cross-correlation. Stability in the Time Domain. GUI Modules and Case Studies. Chapter Summary. Problems. Analysis. GUI Simulation. MATLAB® Computation.
3. Discrete-time Systems in the Frequency Domain.
Motivation. Satellite Attitude Control. Modeling the Vocal Tract. Z-transform Pairs. Region of Convergence. Common Z-transform Pairs. Z-transform Properties. General Properties. Causal Properties. Inverse Z-transform. Noncausal Signals. Synthetic Division. Partial Fractions. Residue Method. Transfer Functions. The Transfer Function. Zero-state Response. Poles, Zeros, and Modes.
DC Gain. Signal Flow Graphs. Stability in the Frequency Domain. Input-output Representation. BIBO Stability. The Jury Test. Frequency Response. Frequency Response. Sinusoidal Inputs. Periodic Inputs. System Identification. Least-squares Fit. Persistently Exciting Inputs. GUI Modules and Case Studies. Chapter Summary. Problems. Analysis. GUI Simulation. MATLAB® Computation.
4. Fourier Transforms and Spectral Analysis.
Motivation. Fourier Series. DC Wall Transformer. Frequency Response. Discrete-time Fourier Transform (DTFT). DTFT. Properties of the DTFT. The Discrete Fourier

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