Discrete-Time Signal Explorer
Disclaimer: This was built with the help of ClaudeAI as an educational tool for Foundations of Digital Signal Processing Discrete-Time Signal Explorer […]
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Sampling
Sampling: Continuous-to-discrete What is Sampling? Sampling is the process of converting a continuous-time signal into a discrete time signal. Sampling is accomplished by […]
Filter Properties
Filter Properties and their Pole-Zero Plots The transfer function represents a characteristic of a linear, time-invariant system (or filter). We can determine […]
Frequency Selective Filters
Filter Types from Poles and Zeros In general, the poles and zeros relate to the frequency response in that the angle (in […]
The Fourier Transform Properties
The following tables illustrate the Fourier transform properties. Notice a close similarity between the each of the different transforms. Continuous-Time Fourier Series […]
Poles and Zeros / Causality / Stability
Stability and Feedback Stability A system is asymptotically stable if the region of convergence includes the unit circle. As a result, a […]
Inverse Z-Transform
Motivation One of the challenges with Z-transform is that that inverse is not unique. A single z-transform representation can correspond have multiple […]
Z-Transform
Motivation We previously demonstrated that we can express any linear, time-invariant system with convolution or as difference equations. Yet, these representations can […]
The Discrete-Time Fourier Transform
Discrete-Time Energy Signals For the discrete-time Fourier transform, we can express any discrete-time, energy (aperiodic) signal as a continuous summation (i.e., an integral) of […]
Continuous-Time Fourier Transforms
Representation Theory An important concept from signal processing is that we can often uniquely and completely represent a signal as a weighted […]