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CMDimCircuits.SignalProcessing: {T⇔F}-Domain Analysis Tools

Principal Types

  • DataTime: Represents a time-domain signal, x(t), with a constant time step.
  • DataFreq: Represents a frequency-domain signal, x(t), with a constant frequency step.
  • DataHR{DataTime/DataFreq}: A collection of data with hyper-rectangular organization.
  • Pole(v, :rad/:Hz): Creates a pole object, in rad/s or Hz.
  • Index(v): Creates an index value (identifies a number as an integer-valued index, or span).

More on: DataTime/DataFreq/(DataTF)

DataTime & DataFreq are merely wrapper objects pointing to DataTF for dispatch purposes.

  • The idea is that DataTF initially stores either time or frequency information for the signal.
  • Later, when it is required, the complementary information is lazily generated in DataTF.

Thus, the structure of DataTF ensures the fft/ifft of a signal does not have to be called more than once.

NOTE:

  • DataTime/DataFreq signals only support constant time/frequency steps.
  • DataTime/DataFreq signals can be tagged as either time-periodic, or aperiodic.
    • Depending on the case, proper scaling will be used to represent either the Fourier series coefficients (fcoeff), or a sampling of the frequency spectrum (fspectrum).

Function Listing

Frequency Domain

  • timespace(::Symbol, ::Number, ::Symbol, ::Number): Generates a range representing time.
    • timespace(:ts, [SAMPLING_PERIOD], :tfund, [PERIOD_OF_FUNDAMENTAL]): Guarantees accuracy of ts & verifies tfund.
    • timespace(:tfund, [PERIOD_OF_FUNDAMENTAL], :ts, [SAMPLING_PERIOD]): Targets a value of tfund & verifies applicability of ts.
  • timedomain(::DataFreq): Returns a DataTime (performs ifft(), if necessary).
  • step(): Generates a step response.
    • step(reftime::DataTime, [::Pole,] ndel::Index=[DELAY_TSTEPS], amp=[AMPLITUDE]): Discrete time (drop ::Pole to get ideal response).
    • step(reftime::DataF1, ::Pole, tdel=[DELAY_TIME], amp=[AMPLITUDE]): Continuous time.
  • pulse(): Generates a pulse response.
    • pulse(reftime::DataTime, [::Pole,] ndel::Index=[DELAY_TSTEPS], amp=[AMPLITUDE], tpw::Index=[PULSE_WIDTH]): Discrete time (drop ::Pole to get ideal response).
    • pulse(reftime::DataF1, ::Pole, tdel=[DELAY_TIME], amp=[AMPLITUDE], tpw=[PULSE_WIDTH]): Continuous time.
  • prbs(reglen=[LFSR_REG_LEN], seed=[SEED], nsamples=[NUM_OUTPUT_SAMPLES]): Generates PRBS sequence.
  • pattern(): Generates pattern from a bit sequence.
    • pattern(seq::Vector, pulseresp::DataTime, nbit::Index=[TSTEPS_PER_BIT_PERIOD]): Discrete time.
    • pattern(seq::{Vector/DataF1}, pulseresp::DataF1, tbit::Index=[BIT_PERIOD]): Continuous time.
  • datavec(::Symbol, ::DataMD): Accessor for a base vector.
    • datavec(:time, ::{DataTime/DataFreq}): Returns the time vector.
    • datavec(:freq, ::{DataTime/DataFreq}): Returns the frequency vector.
    • datavec(:sig, ::DataTime): Returns the signal vector (x(t)).
    • datavec(:sig, ::DataFreq): Returns the signal vector (X(f)).

Time Domain

  • freqdomain(::DataTime): Returns a DataFreq (performs fft(), if necessary)
  • fspectrum(::DataFreq): Returns sampled frequency spectrum (non-periodic signals).
  • fcoeff(::DataFreq): Returns Fourier-series coefficients (time-periodic signals).

Known Limitations

  1. Limited support for broadcasting functions over DataHR{DataTime/DataFreq} vectors.