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  • Stu WØSTU

Digital Signal Processing

Manufacturers love to brag about it… Operators tend to love the convenience of it… But very few beginner amateurs have a basic understanding of it!

Digital Signal Processing, or DSP. What is it all about? What does it do for my station?

Before we consider some of the very cool things that DSP can do in our transceiver, let’s make sure we have a little understanding of the whole “digital” thing. Just what is a digital signal? Keeping it practical and related to ham radio, let’s consider the digitization of an RF waveform… from the git go.

Graph of a single sine wave frequency signal.

An RF signal in an electric circuit is an alternating current (AC) signal. That is, the electrons flow back and forth in the circuit at radio frequencies as the voltage reverses polarization, providing electric potential first in one direction and then reversing to the opposite direction. We refer to the polarized voltages as positive and negative voltage. We depict such signals (and their electromagnetic counterparts that are radiated from our antennas) with sine wave forms like that shown to the left, where the amplitude (height) of the wave from the center propagation axis is the instantaneous voltage of the signal as it pulses back and forth.

A single sine wave frequency on an oscilloscope.

Imagine we are measuring this signal, perhaps with a nice oscilloscope that will show us this waveform on its screen. To the left side of the screen is a scale by which we can measure the amplitude (signal voltage) at any position on the waveform. The oscilloscope is providing us an image of the continuous analog wave – by definition, a continuous or unbroken measurement of the wave, and particularly of its amplitude.

But a continuous measurement is difficult to record or represent beyond that nice flowing waveform image. What if we want to represent the waveform with numbers, and specifically, with a limited set of numbers instead of a huge laundry list of values?

We could set our oscilloscope to measure the wave’s amplitude in discrete steps across the waveform, perhaps 10 separate instantaneous measurements per wavelength over equal intervals of time. In the figure below each blue dot represents a point in time of a discrete sample of amplitude. A table of measures is included that indicates how these discrete samples of waveform amplitude can be numerically represented, sampling over time left-to-right across the waveform.

A sine wave signal with ten samples per wavelength indicated.
A periodically sampled signal recreated on an oscilloscope as a stepwise approximation of the sine wave.

If we were to create a waveform strictly from the numerical data in the table it might look something like the oscilloscope image to the right. The amplitude value is updated only with each new discrete measurement, so the waveform takes on a stepwise form – the information between the measurements is lost, but much of the information contained in the waveform is still recoverable, such as amplitudes, frequency, and wavelength information. If we take a lot more samples in the same amount of time, measuring more frequently, we will record a more accurate depiction of the waveform more closely resembling its true smooth form. That will require recording lots more numbers. If we sample too sparsely we reach a threshold at which the numerical information is insufficient to accurately depict the waveform.

Recording discrete measurements like this over time is one form of analog to digital conversion (ADC). The digital signal is simply a list of numbers like in the table above. We can assault the list of numbers with a wide variety of mathematical weapons in our DSP arsenal, forcing the digital waveform to comply with our whims. Of course, in the Digital Signal Processing of a receiver the digital representations are created by sampling with very fast and efficient electronic circuits in lieu of a clunky oscilloscope. The processor itself is much like the microprocessor in a modern personal computer, only optimized for rapid processing of the signal numerical data. Further, after the mathematical processing of the digital signals, the DSP must perform a digital to analog conversion (DAC) so that re-smoothed waveforms are provided to later demodulation stages and ultimately to the receiver’s audio circuits for sound reproduction. By the application of filters, averaging circuits, and other techniques the stepwise digital signal representations are smoothed back into analog signals.

So, a typical Digital Signal Processing system will perform an analog to digital conversion on received signals, operate mathematically on the digital representations, and then perform a digital to analog conversion for modified RF signal output, like this:

Illustration of an analog signal ADC converted for digital processing and then DAC converted back to analog form.

If you have studied the signal processing stream of a heterodyne receiver, as in Section 6.2,Receiving, of the Technician License Course, you’ll recall the block diagram of the receiver’s components and the signal processing accomplished by each stage. And I know you have the burning question in your head, “Just where does this DSP stuff happen in the receiver processing stream?”

The Digital Signal Processing may be applied in a couple of different places and with multiple purposes. Some modern receivers with very fast-sampling electronics will digitize the RF signal immediately -- that is, the digital representation is of the RF signal itself before any analog processing occurs. Often, these receivers are in what is termed a software defined radio (SDR). The RF signal is processed as digital information throughout the demodulation stream, including the processes described below, and finally converted to analog audio signals for sound output.

Other receivers of perhaps slightly older vintage may employ DSP following the intermediate filter (IF) stage. Remember, the IF results from the analog mixing process between RF signals and a variable frequency oscillator, shifting the modulated signal to a much lower frequency on the demodulation path to audio. (See our Heterodyne Receiver article.) The IF is sampled and operated upon in near-real time by the DSP to do any of the following:

  • Filter out undesirable mixing products from the receiver’s IF passband

  • Filter out noise using any of several digital noise reduction algorithms

  • Identify any potential offending strong carrier signals and notch filter it (or them) out of the passband

  • Change the width of the IF passband filter to fit the bandwidth of the operating mode (SSB, CW, AM, or digital mode variations)

  • Provide custom filter shapes and effects as defined by the operator

…and other possible signal processing, depending upon the manufacturers inclusions.

Digital Signal Processing may also be applied in the audio processing stage following the product detector (labeled “Mixer 1” in figure below). While many of the same types of filters and effects can be implemented at this stage as at the IF stage, it is usually more effective to perform those functions at the IF filter stage and avoid passing undesired signals further along the receiver processing path. However, DSP can be readily applied to perform audio functions such as equalizing received audio, audio filtering, audio mixing, and speech processing such as compression or expansion. DSP can be used to provide some of these audio processing features in a transmitter as well, particularly to perform speech processing to enhance your transmitted signal’s intelligibility.

A simplified processing stream of a heterodyne receiver showing the intermediate frequency stage.

The algorithms used in DSP are complex and will not be described in detail in this article. However, let’s consider one light and somewhat simplified view of a commonly implemented technique that will help provide an intuitive understanding of how DSP’s innards work.

Imagine we have a sample of a very complex RF waveform. By applying a mathematical transform known as the Fourier Transform, the waveform’s time-based representation can be converted into a frequency representation. That is, the DSP can compute all the different sine wave component frequencies comprising the complex signal form, as well as the amplitude of each frequency. (See sidenote below.)

A Fourier Transform of an analog signal in the time domain to a frequency domain depiction of component frequencies.

A Fourier Transform Note: Any waveform can be created by a combination of multiple sine wave components of different frequencies and amplitudes. So, any RF signal can be “decomposed” into a larger set of nice sine wave signals. The Fourier Transform shows us the set of frequencies and the amplitude of each that sum together to create a more complex or irregularly shaped signal.

With the digital signal data organized into a frequency spectrum representation, the frequencies may be filtered in many different ways. For example, all frequencies above a desired cutoff value can be digitally eliminated (amplitude value set to zero), and all frequencies below a different cutoff value can be similarly eliminated, thereby leaving only a narrowed desired band of frequencies, as depicted below. The high and low cutoff frequencies define the filter width, or passband. This narrower band may be DA converted back into analog form for further receiver processing, leaving the undesired signals behind.

A frequency domain view of a signal with high and low extremes filtered away.

Imagine that a very narrow spike frequency amplitude exists in this spectrum – a tiny range of frequencies with amplitude much greater than the surrounding frequencies – indicating the presence of an undesired carrier frequency in this band. This scenario is depicted below. The Digital Signal Processing can identify the unusually strong carrier signal by its high amplitude numerical values and use logic to create a filter that sets the amplitude of just that narrow band of unusually strong frequencies to zero. Poof! It’s gone in a puff of digital logic! This is a notch filter, ridding the desired passband of the annoying strong carrier signal.

A frequency domain depiction with a notch filter depicted to filter an interfering carrier signal.

Many other techniques are used in Digital Signal Processing algorithms to implement noise reduction and other functions. DSP can help you bring in those really weak signals from distant stations that you may otherwise miss altogether! If your SSB receiver has DSP features, or if you have a capable software defined radio, read your user’s manual and become familiar with the basic controls and capabilities for using DSP. Now that you have a basic introduction to Digital Signal Processing, you should be able to interpret most of the functions and descriptions. Good luck, and 73!

-- Stu WØSTU


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