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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A cosine wave, square wave, and sine wave all have symmetric rise-and-fall patterns because they are all sums of their sinusoid harmonics, according to Hugh L. Montgomery and Robert C. Vaughan (Multiplicative Number Theory, Cambridge, 2007, p. 536-537).

But a sawtooth wave is an asymmetric triangular wave, because its rise time differs from its fall time, making it the correct one.

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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.

*Hint - Sawtooth wave = all harmonics (Sawz-All)

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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.

Unrelated Hint: "dither" when installing satellite dishs is a 'small' adjustment

Specific knowledge hint: Dithering in visual media refers to introducing noise into an image with a limited color pallette to "mix" colors. https://en.wikipedia.org/wiki/Dither

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The term “RMS” stands for “Root-Mean-Squared”. Most books define this as the “amount of AC power that produces the same heating effect as an equivalent DC power”.

By Ohm's Law (\(V=IR\)), Voltage, Intensity (or Current) and Resistance are related. To know voltage, it is sufficient to know current and resistance. By having a complex waveform, there will not be any easy formula to convert AC voltage to RMS Voltage. By measuring the heating effect in a known resistor, we would find the current passing through it, with which we could find the RMS voltage applied to the circuit.

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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.

Silly hint: PEP-to-average contains 2 hyphens, single-sideband contains 1. 2 to 1 is close to the correct answer of 2.5 to 1

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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

The first thing to remember is that PEP to average ratio is not a static value and is determined by the specific signal you are looking at - because of this, it can vary. Looking at the other answers:

• The frequency of the modulating signal - this is a signal used to move speech up to the RF frequency - It's not going to vary over time, so doesn't contribute to finding the ratio.
• The degree of carrier suppression - similar to the above answer, this is a part of the signal that doesn't vary, so won't vary.
• Amplifier gain - again, a mechanism that doesn't vary, so it won't contribute to calculating the answer.

Hint: average speech [KQ4AEY]

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A direct conversion or flash ADC is optimized for speed at expense of almost every other parameter. The ADC requires a comparator 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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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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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.

Hint: Filters generally limit or remove.

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Digital waveforms convey information that has been transcribed into a digital signal. Speech, Video, and other Data are often converted to a digital format so therefore can be transmitted over a digital waveform.

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Digital signals have a fixed number of states. For example, binary signals can only be 0 or 1 (off or on). Because of this, digital signals can be stored, copied, and manipulated without degrading the signal. Every copy of a digital signal is identical to the original.

In contrast, analog signals are continuously variable. Whenever analog signals are stored, copied or manipulated some noise or distortion is always introduced, which degrades the signal. The difference may be very small, but any copy of an analog signal will be different from the original.

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Analog-->Digital, which is to "sample" the signal.

Sampling a signal actually involves recording an amplitude value at a specific point in time and storing the value off as a time:value in a lookup table. This long standing technology extends over many technologies include Compact Disks, MP3 files, etc... The higher the sampling rate, the higher the resolution. With today's resolution, I'm amazed as how some people can still tell the difference between music recorded on vinyl (analog) and CDs (digital).

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