Keywords: adaptive filtering, DSP, gradient descent, LMS, system identification

Summary: This module introduces adaptive filters through the example of system identification using the LMS algorithm. The adaptive filter adjusts its coefficients to minimize the mean-square error between its output and that of an unknown system.

Keywords: autocorrelation, bit-reversed, boxcar, DFT, Discrete Fourier Transform, Discrete Time Fourier Transform, DSP, DTFT, Fast Fourier transform, FFT, Fourier transform, hamming, mainlobe, Power Spectra, Power Spectral Density Estimate, PSD, sidelobe, twiddle-factor, windowing, zero-pad

Summary: You will investigate the effects of windowing and zero-padding on the Discrete Fourier Transform of a signal, as well as the effects of data-set quantities and weighting windows used in Power Spectral Density estimation.

Keywords: autocorrelation, autocovariance, correlation, cross-correlation, DSP, levinson-durbin, linear predicitive coding, speech, speech coding, speech compression, speech synthesis

Summary: Speech analysis and synthesis with Linear Predictive Coding (LPC) exploit the predictable nature of speech signals. Cross-correlation, autocorrelation, and autocovariance provide the mathematical tools to determine this predictability. If we know the autocorrelation of the speech sequence, we can use the Levinson-Durbin algorithm to find an efficient solution ... the speech. [Expand Summary] Speech analysis and synthesis with Linear Predictive Coding (LPC) exploit the predictable nature of speech signals. Cross-correlation, autocorrelation, and autocovariance provide the mathematical tools to determine this predictability. If we know the autocorrelation of the speech sequence, we can use the Levinson-Durbin algorithm to find an efficient solution to the least mean-square modeling problem and use the solution to compress or resynthesize the speech. [Collapse Summary]

Keywords: DSP, fractional arithmetic, overflow, two's complement

Summary: Two's-complement notation is a mathematically convenient way of representing signed numbers in microprocessors. The most significant bit of a two's complement number represents its sign, and the remaining bits represent its magnitude. Fractional arithmetic allows one to multiply numbers on an integer processor without incurring overflow. Fractional ... one bit. [Expand Summary] Two's-complement notation is a mathematically convenient way of representing signed numbers in microprocessors. The most significant bit of a two's complement number represents its sign, and the remaining bits represent its magnitude. Fractional arithmetic allows one to multiply numbers on an integer processor without incurring overflow. Fractional arithmetic requires sign-extension of multipliers and multiplicands, and it requires the product of two numbers to be left-shifted one bit. [Collapse Summary]

Keywords: BPSK, carrier recovery, coherent demodulation, digital communications, DSP, interpolation, numerically-controlled oscillator, phase-locked loop, QPSK, voltage-controlled oscillator

Summary: The phase-locked loop (PLL) is a critical component in coherent communications receivers that is responsible for locking on to the carrier of a received modulated signal. A PLL adjusts the phase of a numerically-controlled oscillator to match that of the received signal. You will simulate a carrier recovery ... the DSP. [Expand Summary] The phase-locked loop (PLL) is a critical component in coherent communications receivers that is responsible for locking on to the carrier of a received modulated signal. A PLL adjusts the phase of a numerically-controlled oscillator to match that of the received signal. You will simulate a carrier recovery sub-system in MATLAB and then implement the sub-system on the DSP. [Collapse Summary]