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Subelement E7
Section E7F
DSP filtering and other operations; Software Defined Radio Fundamentals; DSP modulation and demodulation
What is meant by direct digital conversion as applied to software defined radios?
  • Software is converted from source code to object code during operation of the receiver
  • Incoming RF is converted to a control voltage for a voltage controlled oscillator
  • Incoming RF is digitized by an analog-to-digital converter without being mixed with a local oscillator signal
  • A switching mixer is used to generate I and Q signals directly from the RF input

In state of the art SDR Radios, RF is received and sent directly to an analog-to-digital (A/D) converter. In other words the RF is digitized and processed by digital circuits from that point.

There are no mixers. local oscillators or intermediate frequencies, avoiding distortion and other undesired effects of mixing. This is a major benefit of SDR receivers.

Direct conversion, RF to digital is the modern trend in amateur radio receivers and transmitters.


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What kind of digital signal processing audio filter is used to remove unwanted noise from a received SSB signal?
  • An adaptive filter
  • A crystal-lattice filter
  • A Hilbert-transform filter
  • A phase-inverting filter

An adaptive filter is used in digital signals processing (DSP) to remove unwanted "audio" noise in single-sideband (SSB).

Hint: "adaptive is for audio"

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What type of digital signal processing filter is used to generate an SSB signal?
  • An adaptive filter
  • A notch filter
  • A Hilbert-transform filter
  • An elliptical filter

Hint: Transforms.

Extract from here: Single Sideband (SSB) Modulation is an efficient form of Amplitude Modulation (AM) that uses half the bandwidth used by AM. This technique is most popular in applications such as telephony, HAM radio, and HF communications, i.e., voice-based communications. This example shows how to implement SSB Modulation using a Hilbert Transformer.

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What is a common method of generating an SSB signal using digital signal processing?
  • Mixing products are converted to voltages and subtracted by adder circuits
  • A frequency synthesizer removes the unwanted sidebands
  • Emulation of quartz crystal filter characteristics
  • Combine signals with a quadrature phase relationship

SSB has the mathematical form of quadrature amplitude modulation (QAM) in the special case where one of the baseband waveforms is derived from the other.


I find the word quadrature to be odd. So I remembered it as the right answer.

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How frequently must an analog signal be sampled by an analog-to-digital converter so that the signal can be accurately reproduced?
  • At half the rate of the highest frequency component of the signal
  • At twice the rate of the highest frequency component of the signal
  • At the same rate as the highest frequency component of the signal
  • At four times the rate of the highest frequency component of the signal

This is a fundamental mathematical limitation of digital signal processing, called the Nyquist theorem. In order to properly reproduce a sampled signal, it must be sampled at a rate (called the Nyquist rate) at least twice as high in frequency as the highest frequency component of the signal.

In addition to this, if you have an analog-to-digital (ADC) converter that samples at \(x\) Hz, the input analog signal must have all frequencies above \(x/2\) Hz filtered out or else those frequencies will "alias" down into the desired frequencies.

A more common example of this might be digital audio, which is sampled at 44.1 kHz, allowing 22.05 kHz (well above human hearing range) to be the highest pitch that can be reproduced. If you tried to sample audio that contained a 23 kHz tone, it would alias down as noise at 21.1 kHz.

A decent rundown of the Nyquist theorem can be found here.

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What is the minimum number of bits required for an analog-to-digital converter to sample a signal with a range of 1 volt at a resolution of 1 millivolt?
  • 4 bits
  • 6 bits
  • 8 bits
  • 10 bits

To sample 1 mV out of a 1 V (1000 mV) signal requires a granularity of 1000 mV / 1 mV = 1000:1 resolution.

9 bits allows for 512:1 resolution (\(2^9 =512\)), which is less than adequate and 10 bits allows for 1024:1 resolution (\(2^{10} =1024\)), which is slightly more than adequate, so the minimum number of bits required is 10 bits.

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What function can a Fast Fourier Transform perform?
  • Converting analog signals to digital form
  • Converting digital signals to analog form
  • Converting digital signals from the time domain to the frequency domain
  • Converting 8-bit data to 16 bit data

Fourier was a mathematician that developed a formula to convert a time-domain signal (amplitude with respect to time) into frequency-domain (relative amplitude or power with respect to frequency). The Fourier transform is rather complicated, but a computer can calculate a short-cut version based on digital samples called the "Fast" Fourier Transform, or FFT.

The display on a spectrum analyzer is the output of the FFT function.

Test Tip: Correct answer is the only one with the word “domain.”

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What is the function of decimation with regard to digital filters?
  • Converting data to binary code decimal form
  • Reducing the effective sample rate by removing samples
  • Attenuating the signal
  • Removing unnecessary significant digits

Decimation refers to destruction (to decimate) of information. Specifically to remove digital samples from a stream of samples of an analog signal. If not done properly, it can lead to aliasing noise.

A decimator, which is what a system component that does this process is called, is typically employed to reduce the data capacity requirements when a signal is sampled at a relatively high sample rate (oversampled). In these situations, an analog signal is sampled at a very high rate, and then filtered in the digital domain to remove noise or high-frequency components, which can be significantly more efficient than analog filters, and then decimated to a lower effective sample rate to reduce the amount of data required to reliably regenerate the signal.

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Why is an anti-aliasing digital filter required in a digital decimator?
  • It removes high-frequency signal components which would otherwise be reproduced as lower frequency components
  • It peaks the response of the decimator, improving bandwidth
  • It removes low frequency signal components to eliminate the need for DC restoration
  • It notches out the sampling frequency to avoid sampling errors

Digital sampling of an analog signal must be done at twice the rate of the highest frequency component of the signal. This is called the Nyquist theorem or Nyquist rate. If samples are removed from a stream of samples making the effective sample rate lower than the Nyquist rate of the signal, all frequency components higher than the nyquist frequency of the new sample stream must be removed (filtered out) before the samples are dropped.

For example, if you had an analog signal with 10kHz as the highest frequency component of the signal, it must be sampled at least 20,000 times per second. If you then were to drop every 2nd (every other) sample (10,000 samples per second effective rate), you would first have to filter out every frequency component above 5kHz in the original signal or else they would alias down as noise into regenerated signal.

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What aspect of receiver analog-to-digital conversion determines the maximum receive bandwidth of a Direct Digital Conversion SDR?
  • Sample rate
  • Sample width in bits
  • Sample clock phase noise
  • Processor latency

The Nyquist Sampling Theorem states that to faithfully represent an analog signal in discrete time, the sample rate must be greater than twice the highest frequency component of interest. Applying this to a Direct Digital Conversion receiver, it means that the receive bandwidth must be less than half of the sample rate. Therefore, the sample rate limits the maximum receive bandwidth of a Direct Digital Conversion SDR (Software Defined Radio).


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What sets the minimum detectable signal level for an SDR in the absence of atmospheric or thermal noise?
  • Sample clock phase noise
  • Reference voltage level and sample width in bits
  • Data storage transfer rate
  • Missing codes and jitter

If there is no noise floor (ideally), there will be nothing to compare the intelligence of the signal to. Using a voltage level along with sampling, the intelligence (signal) can be detected.

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What digital process is applied to I and Q signals in order to recover the baseband modulation information?
  • Fast Fourier Transform
  • Decimation
  • Signal conditioning
  • Quadrature mixing

The FFT (Fast Fourier Transform) in the software-defined radio (SDR) paradigm is one of the few methods for demodulation functions as well as many other radio systems for demodulation of many types of digital signals.

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What is the function of taps in a digital signal processing filter?
  • To reduce excess signal pressure levels
  • Provide access for debugging software
  • Select the point at which baseband signals are generated
  • Provide incremental signal delays for filter algorithms

Hint: Only one answer has the word "delay" in it.

From: https://en.wikipedia.org/wiki/Electronic_filter "Engineers realized that a large number of crystals could be collapsed into a single component, by mounting comb-shaped evaporations of metal on a quartz crystal. In this scheme, a "tapped delay line" reinforces the desired frequencies as the sound waves flow across the surface of the quartz crystal. The tapped delay line has become a general scheme of making high-Q filters in many different ways."

More taps increase the steepness of the filter roll-off while increasing calculation time (delay) and for high order filters, limiting bandwidth.

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Which of the following would allow a digital signal processing filter to create a sharper filter response?
  • Higher data rate
  • More taps
  • Complex phasor representations
  • Double-precision math routines

Tap - A FIR "tap" is simply a coefficient/delay pair. The number of FIR taps, (often designated as "N") is an indication of 1) the amount of memory required to implement the filter, 2) the number of calculations required, and 3) the amount of "filtering" the filter can do; in effect, more taps means more stopband attenuation, less ripple, narrower filters, etc.


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Which of the following is an advantage of a Finite Impulse Response (FIR) filter vs an Infinite Impulse Response (IIR) digital filter?
  • FIR filters delay all frequency components of the signal by the same amount
  • FIR filters are easier to implement for a given set of passband rolloff requirements
  • FIR filters can respond faster to impulses
  • All of these choices are correct

Finite Impulse Response (FIR) filters and Infinite Impulse Response (IIR) filters are both discrete-time filters, but one major difference is that IIR filters include a feedback path whereas FIR filters do not. Without feedback the effects of any input signal cannot persist longer than the fixed delay of the filter. In an FIR filter all input samples are treated equally. They all proceed through the same tapped delay line and fall off the end after a fixed amount of time. Because of this, all frequency components of the input signal are delayed by the same amount of time.


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How might the sampling rate of an existing digital signal be adjusted by a factor of 3/4?
  • Change the gain by a factor of 3/4
  • Multiply each sample value by a factor of 3/4
  • Add 3 to each input value and subtract 4 from each output value
  • Interpolate by a factor of three, then decimate by a factor of four

Sample rate can be modified by two mechanisms.

Interpolation is the process of increasing sample rate by estimating what the samples between two known samples.

Decimation is the process of decreasing sample rate by dropping samples.

The point of this question is that if you want to do non-integer sample-rate change, you can accomplish it by interpolation at one factor followed by decimation at another factor. The important thing to remember is that with decimation, information is lost, but with interpolation, it is not. So you should do the interpolation before the decimation, since when you decimate a digital signal, you have to filter out information from the original signal.

Using the questions 3/4 sample-rate change, interpolation by a factor of three, and then decimation by a factor of 4 will result in a signal that could lose at most 1/4 of it's information. If the decimation by a factor of 4 were applied first, it would have have 75% of the signal information filtered out, at which point you're interpolating from lost information.

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What do the letters I and Q in I/Q Modulation represent?
  • Inactive and Quiescent
  • Instantaneous and Quasi-stable
  • Instantaneous and Quenched
  • In-phase and Quadrature

Amplitude and phase can be modulated simultaneously and separately to convey more information than either alone, but it isn't easy to do.

A simpler way is to separate the original signal into a set of independent components or channels:
   I (In-phase) and Q (Quadrature).

The I and Q components are considered orthogonal, or in quadrature, because they are separated by 90 degrees. The I and Q components are then added together in a modulator circuit.

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