Breakthroughs in Signal Processing#
These landmarks trace a conceptual development from a physical law to a useful engineering model. The order is a learning path, not a dated chronology or a claim that any idea had a single inventor. SI units apply unless documented otherwise.
Fourier: a waveform has a frequency description#
Decomposing a signal into complex exponentials makes filtering and spectral analysis tractable. A finite record and a window alter the displayed spectrum.
Use engineeringkit.signal_processing.dft to explore the model.
FFT bins are a finite-record representation; leakage and normalization must be considered.
Sampling: information can be lost before filtering#
Sampling creates indistinguishable frequencies separated by integer multiples of the sample rate. Band-limited reconstruction requires an adequate rate and antialias filtering before digitization.
Use engineeringkit.signal_processing.alias_frequency to explore the model.
Finite sinc reconstruction is truncated; samples cannot reveal an already aliased original frequency.
Digital filtering: system memory is explicit#
Convolution connects an input to an impulse response. FIR and IIR implementations trade finite memory against recursive structure and phase behavior.
Use engineeringkit.signal_processing.filter_signal to explore the model.
These helpers use causal forward filtering with default initial state, so startup transients and phase delay remain.
Explore and verify#
Signal processing: sampled energy, spectra and quantization records units, conventions and independent checks. Compare the gallery output against the equations before extending a model.
Further reading#
University or agency teaching reference provides background beyond the implemented subset. The equations and examples here are concise original explanations, not reproductions of that reference.