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Subelement E7

PRACTICAL CIRCUITS

Section E7F

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

What is meant by “direct sampling” in software defined radios?

  • Software is converted from source code to object code during operation of the receiver
  • I and Q signals are generated by digital processing without the use of RF amplification
  • Correct Answer
    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.

HINT: The correct answer is the only one with language about digital. i.e analog-to-digital and digitized

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

  • Correct Answer
    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
  • Correct Answer
    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.

Hint: think Single-Side(B)and: Hil(B)ert

— serif

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Which method generates an SSB signal using digital signal processing?

  • Mixing products are converted to voltages and subtracted by adder circuits
  • A frequency synthesizer removes unwanted sidebands
  • Varying quartz crystal characteristics are emulated in digital form
  • Correct Answer
    Signals are combined in 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.

https://en.wikipedia.org/wiki/Single-sideband_modulation#Mathematical_formulation

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

  • At least half the rate of the highest frequency component of the signal
  • Correct Answer
    At least 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.

Hint: A wavelength is composed of a positive half and a negative half. Digitally, this is minimally represented as one 1 and one 0 - two bits. Therefore the sampling frequency must be at least two times the frequency of the signal.

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

  • 4 bits
  • 6 bits
  • 8 bits
  • Correct Answer
    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.

Hint: 1V, 1mV, and 10bits are all multiples of 10.

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What function is performed by a Fast Fourier Transform?

  • Converting analog signals to digital form
  • Converting digital signals to analog form
  • Correct Answer
    Converting signals from the time domain to the frequency domain
  • Converting signals from the frequency domain to the time domain

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.”

Test Tip: The question mentions "fast," which suggests the answer containing the word "time."

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What is the function of decimation?

  • Converting data to binary-coded decimal form
  • Correct Answer
    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.

Memory Hint: In your head think "de-cimation" = "de-sample". Remove samples.

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

  • Correct Answer
    It removes high-frequency signal components that 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.

Hint: To Decimate Something is to Remove It from Existance

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

  • Correct Answer
    Sample rate
  • Sample width in bits
  • Integral non-linearity
  • Differential non-linearity

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).

Recall that

\[\text{BW} = \frac{f}{Q}\]

\[\text{bandwidth} = \frac{\text{frequency}}{\text{Q}}\]

Hint: Receiver Analog-To-digital = "RATe"

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

  • Sample clock phase noise
  • Correct Answer
    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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Which of the following is generally true of Finite Impulse Response (FIR) filters?

  • Correct Answer
    FIR filters can 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 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.

Stupid test hint: A finite value is a fixed amount. So, you should pick the answer with the word amount in it :)

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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
  • Correct Answer
    Provide incremental signal delays for filter algorithms

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

From: https://en.wikipedia.org/wiki/Filter_(signal_processing)#Quartz_filters_and_piezoelectrics "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.

Study hints:

  • Both the question and the answer have the word "filter" in them.
  • Tap the digital (clock) to delay (snooze) the alarm.

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

  • Higher data rate
  • Correct Answer
    More taps
  • Lower Q
  • 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.

http://dspguru.com/dsp/faqs/fir/basics

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