Generate audio that displays readable text when viewed as a spectrogram.

The idea

A spectrogram is a time-frequency picture of a signal: the x-axis is time, the y-axis is frequency, and brightness encodes magnitude. If we place sine waves at specific frequencies during specific time intervals, we can "draw" in the spectrogram. Given a short string like "HELLO", the library rasterises it with a tiny bitmap font, maps each pixel to a frequency band, and synthesises the corresponding tones. The result is a WAV file that sounds like a buzzy chord but reveals the hidden message visually.

How it works

Bitmap font — Each printable ASCII character (32–126) is stored as a 5-column, 7-row bitmap. One byte per column, one bit per row. Characters are spaced three columns apart, giving a grid width of \( W = 8 \times \mathrm{len} - 3 \) columns and 7 rows.

Frequency mapping — Row 0 maps to freq_hi (top of the spectrogram), row 6 maps to freq_lo (bottom). Intermediate rows are linearly interpolated:

\[f_r = f_\mathrm{hi} - \frac{r}{6} \, (f_\mathrm{hi} - f_\mathrm{lo}) \]

Reading the formula in C:

// f_hi -> freq_hi,  f_lo -> freq_lo,  r -> r,  f_r -> row_freq[r]
// The font has 7 rows, so the denominator is 6 (= 7 − 1).
double row_freq[7];
for (unsigned r = 0; r < 7; r++)
    row_freq[r] = freq_hi - (double)r / 6.0 * (freq_hi - freq_lo);

Synthesis — Each bitmap column occupies col_samples = duration / W * sample_rate audio samples. For every "on" pixel in that column a sine wave at frequency \( f_r \) is added. Phase is carried continuously across columns so that sustained tones (adjacent "on" pixels in the same row) produce a smooth sinusoid.

Crossfade — A 3 ms raised-cosine ramp is applied at tone onsets and offsets (transitions between adjacent "on" and "off" columns in the same row) to suppress broadband clicks.

Normalisation — After all columns are synthesised the entire signal is scaled so that the peak absolute amplitude is 0.9.

API

unsigned MD_spectrogram_text(double *output, unsigned max_len,
                             const char *text,
                             double freq_lo, double freq_hi,
                             double duration_sec, double sample_rate);

Parameters:

Parameter	Description
output	Caller-allocated buffer for the synthesised audio.
max_len	Size of output in samples (must be >= returned value).
text	Printable ASCII string to render (non-empty).
freq_lo	Lowest frequency in Hz (bottom of text in spectrogram).
freq_hi	Highest frequency in Hz (top of text in spectrogram).
duration_sec	Total signal duration in seconds.
sample_rate	Sample rate in Hz (freq_hi must be < sample_rate / 2).

Returns the number of samples written.

Quick example

#include "minidsp.h"
 
double buf[64000];
unsigned n = MD_spectrogram_text(buf, 64000, "HELLO",
                                 200.0, 7500.0, 2.0, 16000.0);
/* buf[0..n-1] contains the audio.  Compute its STFT to see "HELLO". */

Example program

The example examples/spectrogram_text.c generates a WAV file, an interactive HTML spectrogram, and a static PNG image.

Usage:

./spectrogram_text [TEXT] [--colormap hot|grayscale]

Default text is "HELLO", default colormap is hot.

Synthesis and STFT parameters used by the example (so you can replicate the spectrogram with your own tools):

Parameter	Value
Sample rate	16000 Hz
Frequency range	400–7300 Hz
Duration	2.25 s
Silence padding	0.5 s before/after (default)
STFT FFT size	1024
STFT hop	16 samples (1 ms)
dB range	−80 to 0 dB
Colorscale	Hot (or grayscale)

Outputs: spectrogram_text.wav, spectrogram_text.html, spectrogram_text.png.

Viewing the result

Listen — the synthesised "HELLO" (buzzy chord):

Spectrogram — each letter is visible as a cluster of horizontal bands in the time-frequency plane:

Build and run:

make -C examples spectrogram_text
cd examples && ./spectrogram_text "HELLO"
open spectrogram_text.html     # interactive spectrogram
open spectrogram_text.png      # static image