E7F

Software defined radio and DSP

Explain how an SDR samples and processes signals: Nyquist, aliasing, bit depth, FIR filters, SSB generation and the FFT.

14 pool questions1 on the exam

Syllabus: Software defined radio fundamentals: digital signal processing (DSP) filtering, modulation, and demodulation; analog-digital conversion; digital filters

An SDR digitizes early, then does the rest in software

An ADC turns the signal into numbers and a DSP processes them. In direct sampling the incoming RF is digitized without being mixed with a local oscillator. The ADC's sample rate sets the maximum receive bandwidth.

After the ADC the signal is just numbers for software to process. Direct sampling skips the mixer and oscillator.

RememberDirect sampling = ADC straight on the RF, no mixer. Sample rate sets bandwidth.

Sample at least twice the highest frequency

Sample too slowly and a high frequency looks like a lower one: an alias. So the rate must be at least twice the highest frequency, and the usable bandwidth is up to half the sample rate.

Dots are the samples. To reproduce a signal you need at least twice its highest frequency.

Signal frequency7 kHzSample rate10 kS/s

Decimation lowers the sample rate by removing samples. An anti-aliasing filter goes first, to remove the high frequencies that would otherwise be reproduced as lower ones.

Filter first. Without it, the removed frequencies fold down and show up as aliases.

RememberSample at 2× the top frequency or more. Decimate = drop samples, after a low-pass filter.

More bits, finer steps, weaker detectable signals

An n-bit converter has 2ⁿ levels. The smallest step is the reference voltage ÷ 2ⁿ, so reference voltage and bit width set the minimum detectable signal.

More bits, finer steps, weaker signals can be detected. The reference voltage sets the full-scale range.

Sample width10 bits

For 1 V at 1 mV you need 1000 levels: 2⁹ = 512 is too few, 2¹⁰ = 1024 is enough, so 10 bits.

RememberLevels needed = range ÷ resolution. Take the next power of two.

A FIR filter is a delay line with taps. More taps, sharper filter.

A tap is one more incremental delay in the filter. Each tap's copy is weighted and summed. A FIR (finite impulse response) filter can delay all frequencies by the same amount (with symmetric taps). More taps give a sharper response, at the cost of more computing.

Each tap is one more delayed copy of the signal. More taps, more steps to shape the response.

Number of taps31

RememberTaps = incremental delays. More taps = sharper response.

Each DSP tool has one job

Tool	Job
Adaptive filter	removes unwanted noise from received SSB audio
Hilbert-transform filter	makes the 90° copy used to generate SSB
Quadrature combining	one sideband adds, the other cancels
FFT	time domain to frequency domain

Signals combined in quadrature: one sideband adds up, the other cancels. Which one depends on the sign and phase convention.

FFT: time domain in, frequency domain out. Each tone becomes a peak.

RememberAdaptive = noise. Hilbert = make SSB. FFT = time to frequency.

Loading lesson…

Go deeper

Compendium articles on the ideas in this lesson, beyond what the exam asks.

Check what stuck

Practise the 14 pool questions for this group. Answers are shuffled, and every one comes with a one-line "why".

Practise E7F →