E7F: SDR Fundamentals

Software-defined radio (SDR) replaces traditional analog signal processing with digital computation. Signals are digitized as early in the receive chain as possible, and virtually all filtering, demodulation, and decoding is done in software. This approach allows one piece of hardware to handle many different modes and frequencies, and it has transformed modern amateur radio equipment.

This lesson covers direct sampling, the Nyquist sampling theorem, analog-to-digital conversion, FFT, decimation, anti-aliasing, FIR filters, Hilbert transforms, quadrature signal generation, and DSP filter characteristics including taps.

Direct Sampling

Direct sampling in software defined radios means that incoming RF is digitized by an analog-to-digital converter (ADC) without first being mixed with a local oscillator signal. This is a fundamental departure from traditional superheterodyne receivers that convert the RF to an intermediate frequency before digitizing.

In a direct-sampling SDR, the sample rate of the ADC determines the maximum receive bandwidth. According to the Nyquist theorem, the ADC can faithfully represent signals up to half its sample rate. A 50 MSPS ADC can handle up to 25 MHz of instantaneous bandwidth.

The minimum detectable signal in a direct-sampling SDR (in the absence of atmospheric or thermal noise) is set by the reference voltage level and sample width in bits. These two factors together determine the quantization noise floor — the smallest signal the ADC can resolve.

Nyquist Theorem and Sampling Rate

The Nyquist-Shannon sampling theorem states that to accurately reproduce a signal, it must be sampled at at least twice the rate of its highest frequency component. For a voice signal with a highest frequency of 3 kHz, the sampling rate must be at least 6 kHz. Sampling below the Nyquist rate causes aliasing — high-frequency components appear as lower-frequency aliases in the digital output.

ADC Bits and Dynamic Range

The number of bits in the ADC determines the resolution of the digital representation. Each additional bit doubles the number of quantization levels and adds approximately 6 dB of dynamic range.

Fast Fourier Transform (FFT)

The Fast Fourier Transform is an efficient algorithm for computing the discrete Fourier transform. Its function is converting signals from the time domain to the frequency domain. Given a block of time-domain samples, the FFT produces a spectrum showing the amplitude and phase of each frequency component present.

In SDR systems, FFTs are used for spectrum display (the waterfall or pan-adapter), for channelization, and as the first step in filter-bank based demodulation. Modern processors can compute FFTs fast enough to analyze wide bands in real time.

Decimation and Anti-Aliasing

Decimation is the process of reducing the effective sample rate by removing samples. If you take every second sample from a 10 MSPS stream, you produce a 5 MSPS stream — the effective rate is halved, and the bandwidth the stream can represent is also halved.

Before decimating, an anti-aliasing filter must be applied. Without it, signal components above the new Nyquist frequency would fold back into the baseband, creating aliases. The anti-aliasing filter removes high-frequency signal components that would otherwise be reproduced as lower frequency components after decimation.

FIR Filters and Taps

A Finite Impulse Response (FIR) filter computes each output sample as a weighted sum of a finite number of past and current input samples. The individual multiplier coefficients are called taps, and their function is to provide incremental signal delays for filter algorithms. Each tap corresponds to one sample delay, and the filter's frequency response is determined by the values assigned to the tap coefficients.

FIR filters have a key advantage: they can be designed to provide linear phase response, which means they delay all frequency components of the signal by the same amount. This preserves signal shape and is important for data communications.

More taps allow a DSP filter to create a sharper filter response — more taps mean more coefficients, which allow steeper roll-off and better stop-band attenuation. The trade-off is increased computation.

An adaptive filter is the type of DSP audio filter used to remove unwanted noise from a received SSB signal. Adaptive filters adjust their coefficients in real time based on the input signal to minimize noise.

Hilbert Transform and SSB Generation

A Hilbert-transform filter is used in DSP to generate SSB signals. It shifts the phase of all frequency components by 90°, creating the quadrature component of a signal. When the in-phase (I) and quadrature (Q) components are combined with appropriate signs, one sideband cancels and the other adds — producing SSB.

The DSP method of SSB generation combines signals in a quadrature phase relationship. The I and Q signal paths are combined with a phase difference that causes one sideband to add constructively and the other to cancel.

E7F Practice Questions