Digital signal processing is the numerical manipulation of sampled signals to filter, transform, detect, compress, modulate, or reconstruct information. Every layer of an AI chip's surrounding system — audio front-ends, radar, image sensors, SerDes PHYs, wireless modems — relies on DSP algorithms implemented in hardware MAC arrays, dedicated DSP cores, or programmable vector engines.
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<!-- ═══ PANEL 1: Sampling & Anti-Aliasing (x=8,y=8,w=234,h=290) ═══ -->
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<text x="125" y="27" text-anchor="middle" class="hdr">Sampling & Anti-Aliasing</text>
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<text x="125" y="44" text-anchor="middle" class="sm dim">Continuous signal x(t)</text>
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<text x="125" y="85" text-anchor="middle" class="sm dim">Sample at fs = 8 kHz (Nyquist: fs > 2·fmax)</text>
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<text x="125" y="124" text-anchor="middle" class="sm dim">↑ discrete samples x[n]</text>
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<text x="125" y="147" text-anchor="middle" class="sm" fill="#3fb950">Nyquist: fs > 2 × fmax</text>
<text x="125" y="161" text-anchor="middle" class="sm dim">fs=8kHz → max signal freq = 4 kHz (voice)</text>
<text x="125" y="172" text-anchor="middle" class="sm dim">ADC anti-alias filter before sampling</text>
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<text x="125" y="204" text-anchor="middle" class="sm" fill="#f85149">Aliasing: fs < 2·fmax → fold-back</text>
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<text x="155" y="222" class="sm" fill="#388bfd">true</text>
<text x="155" y="234" class="sm" fill="#f85149">alias</text>
<text x="125" y="252" text-anchor="middle" class="sm dim">indistinguishable after sampling</text>
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<text x="125" y="265" text-anchor="middle" class="sm" fill="#d29922">Quantization: N bits → SNR ≈ 6N + 1.76 dB</text>
<text x="125" y="278" text-anchor="middle" class="sm dim">16-bit audio: ~98 dB SNR · 12-bit ADC: ~74 dB</text>
<!-- ═══ PANEL 2: FIR Filter (x=250,y=8,w=244,h=290) ═══ -->
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<text x="372" y="27" text-anchor="middle" class="hdr">FIR Filter — Tapped Delay Line</text>
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<!-- Input -->
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<text x="305" y="51" text-anchor="middle" class="sm" fill="#388bfd">z⁻¹</text>
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<!-- Multiplier circles -->
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<text x="275" y="84" text-anchor="middle" class="sm" fill="#d29922">h₀</text>
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<text x="305" y="84" text-anchor="middle" class="sm" fill="#d29922">h₁</text>
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<text x="355" y="84" text-anchor="middle" class="sm" fill="#d29922">h₂</text>
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<text x="405" y="84" text-anchor="middle" class="sm" fill="#d29922">h₃</text>
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<text x="455" y="84" text-anchor="middle" class="sm" fill="#d29922">h₄</text>
<!-- Adder -->
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<text x="365" y="112" text-anchor="middle" class="sm" fill="#3fb950">Σ</text>
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<text x="370" y="128" class="sm dim">y[n]</text>
<!-- Equation -->
<text x="372" y="148" text-anchor="middle" class="sm" fill="#d29922">y[n] = ∑ h[k] · x[n−k] (k=0..N−1)</text>
<text x="372" y="162" text-anchor="middle" class="sm dim">N taps → N multiplications + N−1 additions per output</text>
<!-- Frequency response -->
<text x="372" y="180" text-anchor="middle" class="sm dim">Frequency response H(e^jω) = DFT of h[k]</text>
<!-- Low-pass filter shape -->
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<text x="286" y="212" class="sm" fill="#388bfd">passband</text>
<text x="410" y="260" class="sm dim">stopband</text>
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<text x="340" y="212" class="sm" fill="#f85149">fc</text>
<text x="372" y="286" text-anchor="middle" class="sm dim">LPF shown · HPF/BPF/BSF by coefficient choice</text>
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<text x="627" y="27" text-anchor="middle" class="hdr">FFT — Cooley-Tukey Butterfly</text>
<!-- 8-point FFT: 3 stages, 4 butterflies per stage -->
<!-- Stage labels -->
<text x="532" y="44" class="sm dim">x[n]</text>
<text x="620" y="44" class="sm dim">Stage 1</text>
<text x="665" y="44" class="sm dim">Stage 2</text>
<text x="710" y="44" class="sm dim">X[k]</text>
<!-- Input nodes (bit-reversed order) -->
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<circle cx="532" cy="176" r="4"/><text x="515" y="180" class="sm dim">x[1]</text>
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<circle cx="532" cy="236" r="4"/><text x="515" y="240" class="sm dim">x[3]</text>
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<!-- Stage 1 butterfly connections (8 inputs -> 8 outputs, stride 1) -->
<!-- Butterfly pair 1: nodes 0,1 (y=56,86) -->
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<!-- Stage 2 (stride 2) -->
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<circle cx="700" cy="116" r="4"/><text x="706" y="120" class="sm dim">X[2]</text>
<circle cx="700" cy="146" r="4"/><text x="706" y="150" class="sm dim">X[3]</text>
<circle cx="700" cy="176" r="4"/><text x="706" y="180" class="sm dim">X[4]</text>
<circle cx="700" cy="206" r="4"/><text x="706" y="210" class="sm dim">X[5]</text>
<circle cx="700" cy="236" r="4"/><text x="706" y="240" class="sm dim">X[6]</text>
<circle cx="700" cy="266" r="4"/><text x="706" y="270" class="sm dim">X[7]</text>
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<!-- Complexity note -->
<text x="627" y="284" text-anchor="middle" class="sm dim">N=8: 3 stages × 4 butterflies · O(N log N) vs O(N²) DFT</text>
<!-- ═══ CARDS (y=305, h=158) ═══ -->
<!-- Card 1: DSP Pipeline -->
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<text x="125" y="322" text-anchor="middle" class="lrg">DSP Pipeline</text>
<text x="16" y="338" class="sm dim">Analog → Anti-alias LPF → ADC → DSP core → DAC</text>
<text x="16" y="352" class="sm dim">Key ops: filter, FFT, convolution, correlation</text>
<text x="16" y="366" class="sm" fill="#3fb950">FIR: linear phase, always stable, N MAC/sample</text>
<text x="16" y="380" class="sm" fill="#388bfd">IIR: fewer taps, possible instability, feedback</text>
<text x="16" y="394" class="sm dim">SIMD/VLIW: MAC arrays for parallel filter taps</text>
<text x="16" y="408" class="sm dim">Fixed-point Q-format: 16-bit saves area vs float</text>
<text x="16" y="422" class="sm dim">MAC: Multiply-ACcumulate — the core DSP op</text>
<text x="16" y="436" class="sm dim">CORDIC: trigonometric ops without multipliers</text>
<text x="16" y="450" class="sm dim">Overlap-add: efficient block convolution via FFT</text>
<!-- Card 2: FFT Applications -->
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<text x="372" y="322" text-anchor="middle" class="lrg">FFT Applications</text>
<text x="258" y="338" class="sm dim">Spectrum analysis: find frequency content of signal</text>
<text x="258" y="352" class="sm dim">OFDM (5G/WiFi): parallel subcarrier modulation</text>
<text x="258" y="366" class="sm" fill="#3fb950">N=4096 OFDM → 4096-pt FFT per symbol period</text>
<text x="258" y="380" class="sm dim">Radar: range-doppler map via 2D FFT</text>
<text x="258" y="394" class="sm dim">SONAR, MRI reconstruction, audio compression</text>
<text x="258" y="408" class="sm" fill="#a5d6ff">AI: attention = Q·K^T ≈ convolution (FFT speedup)</text>
<text x="258" y="422" class="sm dim">Monarch Mixer: sub-quadratic attention via FFT</text>
<text x="258" y="436" class="sm dim">Cooley-Tukey: radix-2 DIT/DIF, in-place N log N</text>
<text x="258" y="450" class="sm dim">NVIDIA cuFFT: GPU-accelerated FFT library</text>
<!-- Card 3: DSP in AI Chips -->
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<text x="627" y="322" text-anchor="middle" class="lrg">DSP in AI Chip Context</text>
<text x="510" y="338" class="sm dim">Inference edge: dedicated DSP + NPU cores</text>
<text x="510" y="352" class="sm dim">Audio wake-word: always-on DSP at µW power</text>
<text x="510" y="366" class="sm" fill="#3fb950">Beamforming: FIR filter array across mic elements</text>
<text x="510" y="380" class="sm dim">Image ISP: Bayer demosaic, noise filter, sharpening</text>
<text x="510" y="394" class="sm dim">Radar: CFAR detection, range-doppler 2D-FFT</text>
<text x="510" y="408" class="sm" fill="#a5d6ff">Mixed-signal: ADC/DAC for SerDes, HBM PHY</text>
<text x="510" y="422" class="sm dim">OFDM modem in 5G SoC: FFT/IFFT hardware block</text>
<text x="510" y="436" class="sm dim">MAC array throughput: GOps vs TFLOP/s GPU</text>
<text x="510" y="450" class="sm dim">Qualcomm Hexagon: VLIW DSP + HVX vector ext.</text>
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| Operation | Complexity | Hardware | Application |
|---|---|---|---|
| FIR filter (N taps) | O(N) MAC/sample | MAC array, SIMD | Anti-aliasing, channel EQ |
| IIR filter (N poles) | O(N) MAC/sample | Feedback MAC | Audio, control loops |
| DFT (N-point) | O(N²) | Rare directly | Baseline reference |
| FFT (N-point) | O(N log N) | cuFFT, HW FFT | OFDM, radar, spectrum |
| Convolution | O(N·M) or O(N log N) via FFT | Tensor core, DSP | FIR filtering, image |
Sampling theorem (Nyquist-Shannon) — a continuous signal must be sampled at a rate fs > 2·fmax to be reconstructed without aliasing. An anti-aliasing low-pass filter must remove all energy above fs/2 before the ADC. Violating this causes high-frequency content to fold back into the baseband as aliasing distortion, which is indistinguishable from legitimate signal. For voice (4 kHz bandwidth), fs = 8 kHz is exactly Nyquist; CD audio uses 44.1 kHz for 20 kHz bandwidth plus guard band.
FIR filters implement the convolution y[n] = Σ h[k]·x[n−k] using a tapped delay line: the input signal passes through N delay elements (z⁻¹), each tap is multiplied by a coefficient h[k], and the products are summed. FIR filters are unconditionally stable, have linear phase (constant group delay), and are fully specified by their coefficient vector — which is the sampled impulse response. The price is computational load: an N-tap FIR requires N multiplications and N−1 additions per output sample, which is why SIMD MAC arrays are universal in DSP hardware.
FFT and frequency-domain processing — the Discrete Fourier Transform (DFT) converts N time-domain samples to N complex frequency-domain coefficients. Direct computation costs O(N²); the Cooley-Tukey FFT exploits the DFT's periodicity and symmetry to reduce this to O(N log₂N) using a butterfly network of complex additions and twiddle-factor multiplications. An 8-point FFT requires 3 stages of 4 butterflies; a 4096-point FFT requires 12 stages of 2048 butterflies. OFDM modems (5G, Wi-Fi 6E, DOCSIS) implement 4096-point FFTs as hard IP blocks, processing one symbol per FFT latency.
AI connections — long-range attention in transformer models can be viewed as a form of learned convolution in the sequence domain. Monarch Mixer and other sub-quadratic attention proposals leverage FFT-based convolution (O(N log N)) to replace O(N²) attention. In a more direct sense, every GPU runs cuFFT for spectral analysis workloads, and AI inference chips for edge devices typically include a DSP subsystem for pre-processing sensor data — beamforming, voice activity detection, image ISP — before the neural-network accelerator core.
Fixed-point and quantization — embedded DSP systems represent samples in Q-format fixed-point (e.g., Q1.15 for 16-bit signed) to save area and power versus floating-point. The SNR of a uniform quantizer is approximately 6N + 1.76 dB for N bits, setting ADC resolution requirements: 12-bit gives ~74 dB, 16-bit gives ~98 dB. The same principle applies to AI inference: INT8 quantization trades 24 dB of numeric headroom for 4× throughput and 4× memory bandwidth reduction.
Read DSP through a frequency-domain decomposition lens rather than a time-domain operations lens: almost every DSP algorithm is most clearly understood in terms of which frequency components it preserves, attenuates, or shifts — the filter, the FFT, and the sampling theorem are all fundamentally statements about the frequency axis.
digital signal processingdspdigital signal processorsignal processingmixed signal verification
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