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Subelement E8
SIGNALS AND EMISSIONS
Section E8A
AC waveforms: sine, square, and irregular waveforms; AC measurements; average power and PEP of RF signals; Fourier analysis; analog to digital conversion: digital to analog conversion; advantages of digital communications
What is the name of the process that shows that a square wave is made up of a sine wave plus all its odd harmonics?
Fourier analysis
• Vector analysis
• Numerical analysis
• Differential analysis

Fourier analysis allows for a time domain signal (Anything we can measure as a function of time) to be transformed into the frequency domain. Letting anyone determine what frequency components exist in the signal.

Hint: Squares have Four(ier) sides

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Which of the following is a type of analog-to-digital conversion?
Successive approximation
• Harmonic regeneration
• Level shifting
• Phase reversal

An easy way to remember this one is that analog-to-digital conversion is always an approximation, because the digital version of something is only an approximation of the analog version. The other answers are unrelated to analog-to-digital conversion.

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What type of wave does a Fourier analysis show to be made up of sine waves of a given fundamental frequency plus all its harmonics?
A sawtooth wave
• A square wave
• A sine wave
• A cosine wave

A square wave consists of the fundamental and odd harmonics because it is symmetric.

A sine and cosine wave consist of only the fundamental frequency, so there are no harmonics.

A sawtooth wave consists of the fundamental, odd, and even harmonics. Only asymmetric waves contain even harmonics and this is the only answer which is an asymmetric wave.

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What is "dither" with respect to analog-to-digital converters?
• An abnormal condition where the converter cannot settle on a value to represent the signal
A small amount of noise added to the input signal to allow more precise representation of a signal over time
• An error caused by irregular quantization step size
• A method of decimation by randomly skipping samples

When an analog signal is sampled by an analog to digital converter the digital value is not infinitely precise, but is truncated to a value which can be represented by the digital output. This quantization error prevents us from hearing signals less than 1 least significant bit in peak-to-peak amplitude.

If we add a small amount of uncorrelated noise to the analog signal before it is sampled, this combined signal can cause bit transitions in the output which are statistically proportional to the weak signal. This noise is called "dither" because it causes the least significant bit to fluctuate randomly. By averaging over time the dither can be eliminated and the weak signal recovered.

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What of the following instruments would be the most accurate for measuring the RMS voltage of a complex waveform?
• A grid dip meter
• A D'Arsonval meter
• An absorption wave meter
A true-RMS calculating meter

Hint: ...most accurate for measuring the RMS voltage...

true-RMS must be the most accurate!

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What is the approximate ratio of PEP-to-average power in a typical single-sideband phone signal?
2.5 to 1
• 25 to 1
• 1 to 1
• 100 to 1

Recall that PEP means the peak envelope power.

The peak envelope of a sinusoidal waveform is its peak-to-peak value, which is twice its peak value. After performing the integration, the average value of a sinusoidal waveform is $2 \times \frac{V_p}{\pi}$ $≈$ $0.637 \times V_p$. The ratio of the peak envelope of a sinusoidal waveform to its average value is therefore $\frac{2 \times V_p}{\left(\frac{2 \times V_p}{\pi}\right)} = \pi$, or $3.14$, which is closer to "2.5 to 1" than the other answers.

If the root mean square (RMS) value of the same waveform is considered instead of its average, the ratio of the peak envelope of a sinusoidal waveform to its RMS value is $\frac{2 \times V_p}{V_p \times \frac{\sqrt{2}}{2}}$ $=$ $2 \times \sqrt{2}$ $≈$ $2.8$, which is even closer to "2.5 to 1" than the other answers.

A true SSB signal is not a simple sinusoid, but made of many superimposed sinusoids, making this an approximation.

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What determines the PEP-to-average power ratio of a single-sideband phone signal?
• The frequency of the modulating signal
Speech characteristics
• The degree of carrier suppression
• Amplifier gain

PEP is Peak Envelope Power. it's the highest power passed to the antenna from the transmitter.

PEP-to-average power ratio is determined by the waveform shape made by the voice, thus the characteristics of the modulating signal

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Why would a direct or flash conversion analog-to-digital converter be useful for a software defined radio?
• Very low power consumption decreases frequency drift
• Immunity to out-of-sequence coding reduces spurious responses
Very high speed allows digitizing high frequencies
• All these choices are correct

A direct conversion or flash ADC is optimized for speed at expense of almost every other parameter. The ADC requires a comparative for every possible output code. This limits the number of output bits, since each additional bit will double the complexity of the device.

Since the output can be determined essentially as fast as a compare and a priority encoder can run; flash ADC's can be produced capable of gigahertz sampling rates. High sample rates are required for a software defined radio, since the sample rate of the ADC is often a limiting factor in the bandwidth of the radio.

** Test Tip = Remember that 'The Flash' runs at a 'Very High Speed'

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How many different input levels can be encoded by an analog-to-digital converter with 8-bit resolution?
• 8
• 8 multiplied by the gain of the input amplifier
• 256 divided by the gain of the input amplifier
256

In binary encoding, the number of levels that can be encoded by a certain number of bits is 2 to the power of the number of bits.

2 bits, $2^2$ = 4 levels

6 bits, $2^6$ = $2 \times 2 \times 2 \times 2 \times 2 \times 2$ = 64 levels

For 8 bits, $2^8=256$. So an 8-bit encoded value can be one of 256 numerical values (typically 0-255). The answer is 256.

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What is the purpose of a low-pass filter used in conjunction with a digital-to-analog converter?
• Lower the input bandwidth to increase the effective resolution
• Improve accuracy by removing out-of-sequence codes from the input
Remove harmonics from the output caused by the discrete analog levels generated
• All these choices are correct

There are often times when signals are passed through a low-pass filter before being converted to a digital signal. The purpose of a low-pass filter being used in conjunction with a Digital-To-Analog (D2A) converter is to remove unwanted harmonics from the output caused by the discrete analog levels generated.

-KE0IPR

Hint: Filters generally limit or remove. K0LLO

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Which of the following is a measure of the quality of an analog-to-digital converter?