Spectrogram — Control Systems/Time Frequency

Spectrogram

Control Systems / Time Frequency

The short-time Fourier transform of a stream: a windowed, one-sided transform of the last L samples, taken every hop samples – MATLAB's spectrogram, one column at a time:

X_j[m] = Σ_n w[n]·x[j·hop + n]·e^−i2πmn/L,   m = 0 … L/2

published as the magnitude |X_j|, or as |X_j|² scaled to a power spectral density or a power spectrum.

Ports

• u – the sampled signal. Scalar: one channel and its own window.
• S – the current frame, [L/2+1, 1], one-sided with DC first and Nyquist last. It changes only on a frame sample and holds in between (see Frames and timing).

Parameters

• Window Length – L, the frame and transform length: an even whole number from 4 to 32. Even because a one-sided spectrum needs a Nyquist bin; bounded above because the transform is unrolled at export and its cost grows as L².
• Hop Size – the samples from one frame to the next, 1 to L. MATLAB's noverlap is L − hop.
• Window – Hamming (MATLAB's default), Hann or Rectangular: the symmetric windows MATLAB's hamming() and hann() return, so hamming(8) starts at 0.08.
• Spectrum Type – what each bin carries:
  • Magnitude – |X[m]|, the magnitude of MATLAB's complex s output. Not doubled and not scaled.
  • Power spectral density – |X[m]|² ÷ (f_s·Σw²) with every bin but DC and Nyquist doubled: MATLAB's ps output.
  • Power spectrum – |X[m]|² ÷ (Σw)², doubled the same way: ps with 'power'.
• Bin Spacing – Δf, the frequency step between output bins in hertz; the sampling rate follows as f_s = L·Δf. It is read only by the power-spectral-density scaling, and it is the same parameter under the same name as Welch PSD's.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Frames and timing

A frame is the last L samples, oldest first. The first is taken when the window first fills – at sample L − 1, counting from 0 – and then every hop samples, so the output at sample L − 1 + j·hop is frame j: column j of MATLAB's spectrogram(x, window, L−hop, L). Between frames the output holds the last one, because a wire holds; before the first frame it is all zeros.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The window, the transform's basis and the scale are fixed by the configuration and inlined as numbers, so no generated core computes a sine, a cosine or a division; all five settings are structural, so re-export after changing one.

The three HDL targets form the transforms and the squares in genuine Q16.16; only the Magnitude square root goes through real (simulation-only), exactly as Quaternion Modulus's does; the two squared types are fully synthesizable. Scale the signal into roughly ±1 first: a frame sums L windowed samples and the block then squares or multiplies.

Simulink bridge

None (Support::None). spectrogram is a Signal Processing Toolbox function and that toolbox ships no Simulink library, so there is no path a diagram could name. The bridge reports this block rather than dropping it silently, and it therefore has no parity testbench; code export verification still covers it across all ten languages.

Notes

• Stateful, and discrete by nature: a register of L samples, a frame counter and the held frame.
• Verified against R2026a: for a twenty-sample record at L = 8, hop = 3, f_s = 100, the Magnitude, Power-spectral-density and Power-spectrum frames match MATLAB's to the last printed digit (the source banner carries the numbers).
• It is not Welch PSD. Welch PSD averages several segments and publishes every sample; this block publishes one segment per frame, every hop samples, and is the time axis a spectrum can be watched along.
• No state space. |X| is not linear in the window, so model reduction correctly declines to merge it.