صفحات العروض بالإنجليزية في الوقت الحالي؛ أما الدرس المرتبط بكل عرض فهو بالعربية بالكامل.
كيف تقرأ هذه الصفحات. كل صفحة تبيّن أي أرقامها محسوبة، وأيها مأخوذ من شكل منشور، وأيها توضيحي. وقد أُنتج بعضها بمساعدة الذكاء الاصطناعي وتذكر ذلك على الصفحة نفسها. هي أدوات تعليمية، وليست قياسات لعتاد حقيقي.
التجارب العملية
العروض التفاعلية
Sampling & aliasing playground
من درس الإيهام الترددي
Raise a tone past half the sampling rate and watch — and hear — the pitch come back down. The replica spectrum, the folding map, a real Butterworth anti-alias filter and the wagon-wheel view of the same arithmetic.
Convolution step-through
من درس الالتواء
Build your own x and h by dragging the stems, then walk the lag while h flips, shifts and multiplies. Every product is written out term by term, the algebraic properties are recomputed on your sequences, and a computed room response lets you hear what a convolution is for.
Pole-zero / z-plane explorer
Drag poles and zeros on the z-plane and watch four views move together: magnitude, phase, impulse response and the pole-zero map itself.
DFT / FFT explorer
من درس تعريف DFT وتفسيره
Where spectral leakage comes from: change the tone, the window and the zero-padding, and watch the DFT bins respond.
Spectrum analyzer
من درس لماذا تحويل DFT بطيء
The window figures of merit, computed from the coefficients: equivalent noise bandwidth N·Σw²/(Σw)², coherent gain (Σw)/N, scalloping loss and peak sidelobe level, each shown beside the published Harris (1978) value. Put a tone (plus noise) through a windowed FFT, detect the peak, and read its frequency and its coherent-gain-corrected amplitude 2|X_peak|/Σw. Watch the analyzer's central trade: a narrow window resolves close tones but hides weak ones; a wide one sees the weak tone but merges the close pair.
FIR / IIR filter designer
من درس FIR مقابل IIR
Design the same specification as FIR and as IIR at once, and see the trade-off the lessons describe in words — order, phase linearity and stopband.
Spectrogram / STFT explorer
من درس الطيف الزمني-الترددي
The time-frequency resolution trade-off, made physical: change the window length and overlap and watch what the spectrogram can and cannot resolve.
Detect a signal in noise
من درس الارتباط الذاتي والمتبادل
Bury a known template in seeded Gaussian noise, run the matched filter (a cross-correlation with the template), and watch the peak stand out where the raw record shows nothing. The processing gain 10*log10(N), the output SNR, and the ROC -- P_d against P_fa -- are all computed, with an optional Monte-Carlo overlay that converges onto the analytic curve.
Resample audio
من درس التخفيض (Decimation)
Convert a signal from one sample rate to another by a rational factor L/M -- upsample by L, lowpass, downsample by M. The reduced L/M (48000 → 44100 = 147/160), the new sample count N' = round(N·L/M), and the anti-alias cutoff min(f_s, f_s')/2 are all computed, and zero-order-hold, linear and windowed-sinc interpolation are ranked by their reconstruction error (sinc < linear < ZOH). Downsample a high tone with the anti-alias filter off and watch it fold.