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E7F

PRACTICAL CIRCUITS

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

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E7F011 of 14

What is meant by "direct sampling" in software defined radios?

Why In a direct sampling (direct RF sampling) SDR, the antenna signal is filtered and amplified and then fed straight into a fast analog-to-digital converter, with no analog mixer or local oscillator ahead of it. All frequency conversion, filtering and demodulation then happen numerically in the DSP. This requires an ADC whose sample rate satisfies Nyquist for the highest frequency of interest, which is why direct sampling first became common at HF.
Watch out The choice about a switching mixer producing I and Q describes a quadrature sampling detector (Tayloe mixer), which is exactly the opposite approach because it does use a local oscillator to translate the signal down before digitizing. The source-code-to-object-code option is about compiling software, not signal handling.
Direct sampling = antenna straight to the ADC, no mixer, no LO. The math does the tuning.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F022 of 14

What kind of digital signal processing audio filter is used to remove unwanted noise from a received SSB signal?

Why An adaptive filter continuously adjusts its own coefficients based on the incoming signal, typically using a least-mean-squares (LMS) algorithm. Speech is correlated from sample to sample while random noise is not, so the filter learns to pass the predictable voice content and cancel the unpredictable hiss. This is what radios label as DSP noise reduction or NR, and it can also notch out steady carriers automatically.
Watch out A crystal-lattice filter is a real analog IF filter made of quartz crystals, not DSP at all. A Hilbert transform is used in DSP for generating the 90 degree phase shift needed for SSB modulation and demodulation, not for noise removal.
Noise is random, speech is not: the filter that adapts learns the difference. NR = adaptive.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F033 of 14

What type of digital signal processing filter is used to generate an SSB signal?

Why Single sideband generated digitally normally uses the phasing method: the audio is split into two paths that are identical in amplitude but 90 degrees apart in phase across the whole audio band, then each drives a mixer fed by carriers also 90 degrees apart, so one sideband adds and the other cancels. The DSP block that produces that broadband 90 degree phase shift is the Hilbert transform filter, usually implemented as an FIR filter with antisymmetric coefficients. Without it you would need a very sharp analog filter to remove the unwanted sideband.
Watch out An elliptical filter is a real analog-style filter response with equal ripple in passband and stopband and very steep skirts, useful for filter-method SSB or anti-aliasing, but it shifts phase only incidentally; a notch filter removes a single tone, and an adaptive filter changes its coefficients on the fly for noise or interference reduction.
Hilbert = 90 degrees across all audio frequencies, the phasing-method key to SSB.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F044 of 14

Which method generates an SSB signal using digital signal processing?

Why DSP transmitters build SSB with the phasing method: the audio is split into two paths whose components differ by 90 degrees (a Hilbert transform provides the wideband phase shift), and those in-phase and quadrature signals modulate carriers that are also 90 degrees apart. When the two products are summed, one sideband adds in phase and the other cancels, leaving a single sideband with no crystal filter required. This quadrature I/Q approach is easy in software because exact 90 degree shifts and perfectly matched amplitudes are just arithmetic.
Watch out The idea of converting mixing products to voltages and subtracting them in adder circuits sounds like analog cancellation but it ignores the essential phase relationship, and a frequency synthesizer only sets the operating frequency, it cannot strip a sideband. Emulating crystal characteristics describes the filter method, not what a quadrature modulator does.
SSB in software = I and Q, 90 degrees apart. Quadrature cancels one sideband.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F055 of 14

How frequently must an analog signal be sampled to be accurately reproduced?

Why This is the Nyquist sampling theorem: to reconstruct a signal without ambiguity, the sampling rate must be at least twice the highest frequency present in that signal. So a 3 kHz audio signal needs at least 6 kHz of sampling, and CD audio uses 44.1 kHz to cover hearing out to about 20 kHz. If you sample slower than that, higher frequency components fold back down into the passband as false lower frequencies, an error called aliasing, which is why an anti-alias lowpass filter is placed ahead of the ADC.
Watch out Sampling at the same rate as, or half the rate of, the highest frequency loses the information entirely and produces aliases; four times the highest frequency does work fine in practice but it is more than the theorem requires, and the question asks for the minimum.
Nyquist: sample at 2x the highest frequency. Twice, not once, not four times.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F066 of 14

What is the minimum number of bits required to sample a signal with a range of 1 volt at a resolution of 1 millivolt?

Why An n-bit converter divides its full-scale range into 2^n steps, so resolution = full scale / 2^n. To resolve 1 mV over a 1 V span you need at least 1 V / 1 mV = 1000 distinct steps. Since 2^9 = 512 is too few and 2^10 = 1024 is just enough, 10 bits is the minimum.
Watch out The 8-bit choice gives only 256 steps, which works out to about 3.9 mV per step over a 1 volt range, far coarser than the 1 mV required.
Divide range by resolution, then find the power of 2 that covers it: 1000 steps needs 1024, so 10 bits.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F077 of 14

What function is performed by a Fast Fourier Transform?

Why A Fourier transform decomposes a waveform sampled over time into the set of sinusoidal components that make it up, giving amplitude (and phase) versus frequency. The Fast Fourier Transform is simply an efficient algorithm for computing that discrete transform, which is what lets an SDR build a waterfall or panadapter display from a stream of samples. So its job is to take time-domain samples in and produce a frequency-domain spectrum out.
Watch out Going from the frequency domain back to the time domain is the inverse FFT, a separate operation; converting between analog and digital is the job of the ADC and DAC, which feed the FFT rather than being it.
FFT = time in, frequency out. Add an 'I' for inverse to go back the other way.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F088 of 14

What is the function of decimation?

Why Decimation lowers the effective sample rate of a digital data stream by keeping only every Nth sample and discarding the rest. A decimation factor of 10, for example, turns a 100 kHz sample stream into a 10 kHz stream, which cuts the processing load and data storage needed downstream. It is normally preceded by a low-pass (anti-alias) filter, because after decimation the new Nyquist limit is half the reduced sample rate, and anything above it would fold back as an alias.
Watch out The choice about removing significant digits describes reducing bit depth or word length, which changes amplitude resolution, not sample rate; decimation throws away samples in time, not bits of precision.
Decimate = drop samples, not bits. Roman decimation killed every tenth man; DSP decimation keeps every tenth sample.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F099 of 14

Why is an anti-aliasing filter required in a decimator?

Why Decimation throws away samples to lower the sample rate, which lowers the Nyquist limit to half the new rate. Any signal content above that new limit folds back down into the passband as false lower-frequency signals (aliases), and once folded it cannot be separated from real signals. So a low-pass (anti-aliasing) filter must run before the samples are discarded, removing everything above half the new sample rate.
Watch out The idea of notching out the sampling frequency misses the point: aliasing comes from content above half the sample rate folding down, not from the sampling clock itself appearing in the data, and a single notch would not stop it.
Decimate = lower Nyquist. Filter first, then throw samples away, or highs fold down as fakes.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F1010 of 14

What aspect of receiver analog-to-digital conversion determines the maximum receive bandwidth of a direct-sampling software defined radio (SDR)?

Why In a direct-sampling SDR the RF is digitized straight away, so the Nyquist criterion applies: the highest frequency that can be represented without aliasing is half the sampling rate. Double the sample rate and you double the usable receive bandwidth. The sample rate is therefore the parameter that sets maximum bandwidth, while other converter specs affect signal quality rather than span.
Watch out Sample width in bits is the tempting pick, but the number of bits sets dynamic range and quantization noise floor (roughly 6 dB per bit), not how wide a slice of spectrum you can capture. Integral and differential non-linearity are accuracy errors in the converter's transfer function that create spurious products.
Rate = width of spectrum, bits = depth of dynamic range. Bandwidth stops at half the sample rate (Nyquist).
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F1111 of 14

What sets the minimum detectable signal level for a direct-sampling software defined receiver in the absence of atmospheric or thermal noise?

Why In a direct-sampling receiver the ADC digitizes the antenna signal directly, so the smallest signal it can represent is one least significant bit, and that step size equals the full-scale reference voltage divided by 2^n, where n is the sample width in bits. That quantization step sets the quantization noise floor, so a larger reference voltage spread over fewer bits raises the floor and hides weak signals, while more bits (about 6 dB of dynamic range per bit) lowers it. With no atmospheric or thermal noise present, that quantization floor is what limits the minimum detectable signal.
Watch out Sample clock phase noise and jitter are real problems, but they mainly smear strong nearby signals and degrade close-in dynamic range, much like reciprocal mixing in an analog receiver; they do not define the basic noise floor. Data storage transfer rate is a computing bottleneck, not a sensitivity limit.
Weakest signal = one LSB: Vref divided by 2^bits. About 6 dB more dynamic range per added bit.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F1212 of 14

Which of the following is generally true of Finite Impulse Response (FIR) filters?

Why An FIR filter with symmetric coefficients has exactly linear phase, which means its group delay is constant: every frequency component passing through is delayed by the same number of samples. That preserves waveform shape, which matters for data modes and pulse signals. This linear-phase property is the main reason FIR filters are chosen over IIR designs in SDR work.
Watch out The claims about easier implementation and faster impulse response actually describe IIR filters, which use feedback to get a steep rolloff with far fewer taps but at the cost of nonlinear phase.
FIR = Fixed delay for every frequency (linear phase). IIR = fewer taps, faster, but phase gets warped.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F1313 of 14

What is the function of taps in a digital signal processing filter?

Why A digital filter works by taking the incoming stream of samples, delaying copies of it by one sample period at a time, multiplying each delayed copy by a coefficient, and summing the results. Each of those delay-and-multiply stages is called a tap, so the taps are literally the incremental delays the filter algorithm operates on. More taps means a sharper, more selective response, at the cost of more computation and more delay (latency) through the filter.
Watch out The debugging answer confuses a DSP tap with a hardware test point or a 'tap' on a transformer winding; in DSP the term refers to the delay stages in the filter structure, not to access points.
Tap = delay stage. More taps, steeper skirts, more latency.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E7F1414 of 14

Which of the following would allow a digital signal processing filter to create a sharper filter response?

Why A digital filter computes its output by multiplying a series of stored input samples by coefficients and summing them; each stored sample and coefficient pair is a tap. More taps means the filter has more degrees of freedom to shape the frequency response, giving steeper skirts and better stopband rejection, at the cost of more computation and more delay. Roughly, transition-band sharpness improves in proportion to filter length, so doubling the taps roughly halves the transition width.
Watch out Double-precision math improves numeric accuracy and reduces rounding noise, but it does not make the response steeper; a higher sample rate actually spreads the same number of taps over a wider bandwidth, which tends to make a filter less selective for a given passband.
Taps are like poles in an analog filter: more taps, steeper skirts.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
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