HKN ECE 310 Final Exam Review Session Corey

HKN ECE 310 Final Exam Review Session Corey Snyder Ben Eng

Topics • LSIC Systems and BIBO Stability • Sampling • Impulse Response and Convolution • Discrete Fourier Transform (DFT) • Z-Transform • Fast Fourier Transform (FFT) • DTFT and Frequency Response Circular Convolution • Digital Filter Design • Rate Conversion and Multirate Systems • D/A Conversion

LSIC Systems •

BIBO Stability •

Impulse Response •

Convolution •

Z-Transform •

BIBO Stability Revisited •

Discrete Time Fourier Transform •

Frequency Response •

Magnitude and Phase Response •

Ideal A/D Conversion •

Discrete Fourier Transform •

DFT Properties • Circular shift • Circular modulation • Circular convolution • We must amend our DTFT properties with the “circular” term because the DFT is defined over a finite length signal and assumes periodic extension of that finite signal.

Zero-Padding • We can improve the resolution of the DFT simply by adding zeros to the end of the signal • This doesn’t change the frequency content of the DTFT! • Instead, it increases the number of samples the DFT takes of the DTFT • This can be used to improve spectral resolution

Fast Fourier Transform •

Decimation in Time •

Fast Linear Convolution •

Linear Phase Filters • FIR vs. IIR – is there feedback? Types of FIR Filters: • Type 1 Odd Length and Even Symmetric • Type 2 Even Length and Even Symmetric • Type 3 Odd Length and Odd Symmetric • Type 4 Even Length and Odd Symmetric

Linear Phase Filter Design •

Digital Filter Structure • Direct Form II

Tips for Linear Phase Filter Design •

Upsampling •

Downsampling •

Ideal D/A •

Realizable D/A: Zero-Order Hold •

How does the ZOH Change our Spectrum?

Upsampled D/A •

P 1: CTFT to DTFT

P 2 : Non-unique Digital Frequencies •

P 3: DFT Matrices and the DFT •

P 4: DFT Shift Property •

P 5: Circular Convolution •

P 6 : La Mariposa (The Butterfly)

Butterfly Structure Exercise •

P 7: Zero Padding •

P 8: FIR and IIR Systems •

P 9: Filter Structure •

P 10 : GLP Filters •

P 11 : Window Method •

P 12 : Up, Down, and Around

P 13 : ADC /DSP /DAC/WTF