Fundamentos de Processamento de Sinal

Getting started with the DSP Education kit: LUT-based Real-Time Sine Wave Generation), Basic Analogue Input & Output Using the STM32F746G Disco Board, and Delaying the Signal.

Peer-to-peer learning/assessment on the convolution sum and determination of the impulse response of a system using the cross-correlation. Lab experimentation and assessment using the STM32F7 on challenges including sinusoidal waveform generation, and viewing program output (sinusoidal and noise waveforms).

Conventional pen-and-pencil exercises on sampling and reconstruction of signals. Laboratory experiments on sampling and reconstruction: understanding that filtering effects depend on the frequency response characteristics of the filter (either analog, or discrete-time), understanding the different components in a complete signal processing chain, understanding basic effects of sampling and reconstruction on sinusoidal, rectangular, triangular, and sawtooth waves.

Peer-to-peer learning/assessment on finding the center of gravity of a discrete-time signal using the properties of the Fourier Transform, and on finding the frequency response of a moving average filter by analytical and numerical means. Laboratory experimentation measuring the frequency response of a moving average filter that is implemented to run in real-time on the STM32F746G Discovery board using different (recursive and non-recursive) difference equations. Evaluation of the performance of groups in class.

Peer-to-peer learning/assessment on the frequency-domain characterization of FIR and IIR COMB filters. Laboratory experimentation measuring the frequency response of FIR and IIR COMB filters. Evaluation of the performance of groups in class.

Evaluation of the DMA operation and conclusion on its advantages and differences to interrupt-based transfer of individual samples. Evaluation of the graphical representation capabilities of the STM32F746G board and LCD. Evaluation of the performance of groups in class.

Peer-to-peer learning/assessment on the analysis of a second-order discrete-time system: transfer function, difference equation, frequency response magnitude, phase response. Experimental determination of the frequency response two 2nd-order IIR filters running in real-time on the STM32F746G Discovery board: an All-Pole filter, and an All-Pass filter.

Peer-to-peer learning/assessment on the impact of the frequency response of a discrete-time system on an infinite-length input sinusoidal sequence, and on the input-output alteration of the Signal to Noise Ratio. Design, modification, and measurement of the frequency response of FIR filters running in real-time on the STM32F746G Discovery board: an equiripple linear-phase FIR of order 80, and two modified versions of the designed FIR filter. Experimental determination of the frequency responses of all three filters and comparison to the theoretical ones.

Peer-to-peer learning/assessment on the design and study of the impulse response and frequency response of a discrete-time differentiator and a Hilbert Transformer. Laboratory assessment on the experimental determination of the frequency response of a discrete-time differentiator, and a Hilbert Transformer, and well as their output when the input is a triangular wave or a square wave.

Pen-and-pencil and Matlab-based exercises on the DFT and IDFT with an emphasis on the DFT properties and the time-domain “aliasing” phenomenon as a result of sampling the DFT. Design, analysis, implementation and real-time operation of a 6th-order band-stop filter: design and decomposition of the 6th-order band-stop filter into second-order sections, implementation of 6th-order band-stop filter for real-time operation on the STM32F7 Discovery kit, conversion of the 6th-order band-stop filter into a 6th-order all-pass filter by just acting on the C code implementing the cascade of second-order sections.

Paper-and-pencil/Matlab exercises on the computation of the auto-correlation using the FFT and on the interpretation of the information contained in a spectrogram. Utilization of the FFT in a number of simulation and real-time experiments addressing the leakage phenomenon, the aliasing phenomenon, windowing, and real-time spectrum analysis using both the STM32F7 platform and the oscilloscope.

Peer-to-peer learning/assessment on the DFT representation of a periodic discrete-time signal and on the computation of the autocorrelation function using the definition and FFT-based processing. Laboratory experimentation on adaptive filtering in a system identification configuration exploiting the steepest descent concept, the impact of the adaptation factor (β), and the importance of the bandwidth of the excitation signal. Evaluation of the performance of groups in class.