Sensor Technology and Programming Basics
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Questions and Answers

What do complex numbers represent in terms of signal processing?

  • The duration of the signal
  • The frequency of the sound waves
  • The amplitude and phase of the frequency components (correct)
  • The number of samples in the recording

Which notation represents both magnitude and phase for frequency components?

  • Exponential notation
  • Polar notation (correct)
  • Rectangular notation
  • Harmonic notation

In polar notation, what does the magnitude indicate?

  • The duration of the signal
  • The amplitude of a frequency component (correct)
  • The offset of the sinusoid in time
  • The frequency of the signal

Why are complex numbers particularly useful for digital systems?

<p>They help in the analysis of frequency components (B)</p> Signup and view all the answers

What does the phase angle in polar notation tell us?

<p>The offset of the sinusoid in time (A)</p> Signup and view all the answers

What is the total amount of levels for a 10 bit resolution ADC?

<p>1024 (D)</p> Signup and view all the answers

What is the approximate value of the Least Significant Bit (LSB) for an ADC with a 0 to 5 volts input range at 10 bit resolution?

<p>4.88 mV (A)</p> Signup and view all the answers

What is the maximum quantization error for a 10 bit ADC with a resolution of 4.88 mV?

<p>+- 2.44 mV (D)</p> Signup and view all the answers

How does quantization error typically behave compared to the actual signal?

<p>It resembles random noise (A)</p> Signup and view all the answers

What is the formula used to calculate the LSB for an ADC?

<p>$\frac{5 V}{1024}$ (C)</p> Signup and view all the answers

What determines the number of quantization levels in an ADC?

<p>The resolution in bits (A)</p> Signup and view all the answers

In a 10 bit ADC system, which scenario would lead to a lower maximum quantization error?

<p>Increasing the bit resolution (A)</p> Signup and view all the answers

Which of the following statements is true regarding the relationship between quantization error and the number of bits in an ADC?

<p>More bits decrease quantization error exponentially (C)</p> Signup and view all the answers

What is the primary purpose of the Short-Time Fourier Transform (STFT)?

<p>To analyze non-stationary signals and their frequency changes over time. (A)</p> Signup and view all the answers

How does the STFT process a signal?

<p>It divides the signal into smaller overlapping segments and computes a Fourier transform for each segment. (B)</p> Signup and view all the answers

What limitation does the standard Fourier transform have that is addressed by the STFT?

<p>It lacks a time dimension, providing only frequency information without timing details. (D)</p> Signup and view all the answers

What type of window function is typically applied in the STFT process?

<p>Hamming window function. (B)</p> Signup and view all the answers

What is one advantage of using overlapping segments in STFT?

<p>It helps to capture transient signals more accurately. (D)</p> Signup and view all the answers

In the context of STFT, what is a key characteristic of non-stationary signals?

<p>Their frequency content varies with time. (C)</p> Signup and view all the answers

Which element is crucial for analyzing smaller time windows in STFT?

<p>The time resolution of the segments. (A)</p> Signup and view all the answers

What step immediately follows applying a window function in the STFT process?

<p>Computing the Fourier transform for the windowed segment. (A)</p> Signup and view all the answers

What does the real part of a complex number represent in rectangular notation?

<p>Amplitudes of the cosine waves (A)</p> Signup and view all the answers

In a DFT plot, what does the magnitude spectrum indicate?

<p>The energy of the signal at each frequency (C)</p> Signup and view all the answers

Which of the following best describes the imaginary parts of complex numbers in rectangular notation?

<p>They correspond to the amplitudes of sine waves. (B)</p> Signup and view all the answers

What type of chart is depicted in a DFT plot?

<p>Magnitude versus frequency plot (A)</p> Signup and view all the answers

What mathematical representation is used when expressing complex numbers in rectangular notation?

<p>Real and imaginary parts (C)</p> Signup and view all the answers

What determines the overall repeating pattern of a periodic signal?

<p>Fundamental frequency (A)</p> Signup and view all the answers

What is the relationship between frequency resolution, sampling frequency, and the number of samples?

<p>Frequency resolution = fs / N (A)</p> Signup and view all the answers

Which statement accurately describes periodic signals?

<p>They have a fundamental frequency if they repeat over time. (C)</p> Signup and view all the answers

What effect does an anti-alias filter have on a signal?

<p>It reduces the bandwidth of high-frequency signals (D)</p> Signup and view all the answers

What is the significance of the power line noise in frequency analysis?

<p>It can introduce unwanted harmonics into the signal (C)</p> Signup and view all the answers

Which of the following best describes white noise?

<p>A continuous signal with uniformly distributed frequency content (A)</p> Signup and view all the answers

How is the fundamental frequency of a signal denoted?

<p>f_0 (A)</p> Signup and view all the answers

What characterizes a signal as being periodic?

<p>Repeating itself over a specific time duration (C)</p> Signup and view all the answers

What does the DFT of a cosine wave produce in the frequency domain?

<p>Two peaks at ± f_0 (C)</p> Signup and view all the answers

What is the relationship between the amplitude of the peaks produced by the DFT of a cosine wave and the amplitude of the cosine wave itself?

<p>The amplitude of each peak corresponds to half the amplitude of the cosine wave. (A)</p> Signup and view all the answers

For the function x(t) = cos(2Ï€10t), where are the peaks located in the DFT?

<p>At frequencies ±10 Hz (D)</p> Signup and view all the answers

How is an impulse signal represented mathematically?

<p>x[n] = {1, n = 0; 0, otherwise} (B)</p> Signup and view all the answers

What does the DFT of an impulse signal indicate about its frequency components?

<p>All frequency components are equally present. (B)</p> Signup and view all the answers

Which property of the DFT is demonstrated by the cosine wave?

<p>It shows symmetrical frequency peaks. (D)</p> Signup and view all the answers

What does the negative peak in the DFT of a cosine wave represent?

<p>A reflection of the positive frequency. (B)</p> Signup and view all the answers

For a cosine wave with an angular frequency of ω = 2π10 rad/s, what is its corresponding frequency in Hertz?

<p>10 Hz (D)</p> Signup and view all the answers

Which of the following statements about the DFT of a cosine wave is true?

<p>It appears as discrete delta functions at certain frequencies. (C)</p> Signup and view all the answers

What does the flat shape of the DFT of an impulse signal imply?

<p>The signal comprises all frequencies equally. (A)</p> Signup and view all the answers

Flashcards

What is a spectrum?

A set of complex numbers that describe the amplitude and phase of a sound wave's frequency components. It's particularly useful for analyzing digital recordings and sensor data.

Polar Notation

A way to represent a spectrum by its magnitude and phase.

What does magnitude represent in a spectrum?

The magnitude of a spectral component represents the amplitude or strength of that frequency in the signal.

What does phase angle represent in a spectrum?

The phase angle tells us the offset of a sinusoid from the time origin. It describes the starting point of a frequency component in the sound.

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What is rectangular notation?

Spectra expressed using Cartesian coordinates, listing each frequency component's real and imaginary parts

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LSB (Least Significant Bit)

The smallest change in voltage that an ADC (Analog-to-Digital Converter) can detect and represent.

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Number of Levels in an ADC

The number of distinct voltage levels an ADC can represent, determined by its resolution.

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Quantization Error

The difference between the actual analog voltage and the closest digital value represented by the ADC.

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Random Noise

A type of error in analog to digital conversion, where the error is not correlated with the input signal and appears random.

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ADC Resolution

The number of bits used by an ADC, indicating its ability to distinguish between different voltage levels.

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Input Range of an ADC

The range of input voltages that an ADC can accurately convert.

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LSB Calculation

The formula used to calculate the LSB value in an ADC, where 'Range' is the full input voltage range and 'Number of Levels' is the total number of distinct levels the ADC can represent.

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Maximum Quantization Error

In an ADC with a given resolution, the maximum quantization error is half the LSB value.

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Rectangular Notation

A way to represent complex numbers using two components: a real part and an imaginary part.

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Magnitude Spectrum

A graph showing the strength of different frequencies in a signal. The x-axis represents frequency, and the y-axis represents the magnitude (strength) of each frequency.

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Real Part of a Complex Number

The component of a complex number that corresponds to the amplitude of the cosine wave in a signal.

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Imaginary Part of a Complex Number

The component of a complex number that corresponds to the amplitude of the sine wave in a signal.

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Fundamental frequency

The lowest frequency in a periodic signal that determines the overall repeating pattern.

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Periodicity

A periodic signal repeats itself over time. It has a fundamental frequency.

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Frequency resolution

The resolution of the frequency plot is determined by the sampling frequency (fs) and the number of samples (N).

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White noise

A signal with equal energy across all frequencies. It appears as a flat line in the frequency plot.

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Power line noise

A specific frequency that causes noise, usually at 50Hz or 60Hz, visible as a spike in the frequency plot.

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Anti-alias filter

A filter that removes frequencies above a certain cutoff frequency, preventing aliasing.

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Signal content

The actual frequencies that are present in the signal. You can analyze it on a frequency plot.

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Anti-alias filter roll-off

The drop in amplitude of a frequency as it nears the cutoff frequency of a filter. How quickly it fades out.

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Frequency Domain

A signal's representation in terms of its frequency components. It shows the strength of each frequency present in the signal.

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Discrete Fourier Transform (DFT)

A mathematical transformation that converts a signal from the time domain to the frequency domain.

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Impulse Signal

A signal that is zero everywhere except at a single point in time.

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DFT of a Cosine Wave

The DFT of a cosine wave produces two peaks, one at the positive frequency and one at the negative frequency. The amplitudes of the peaks represent half the amplitude of the original cosine wave.

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DFT of an Impulse

The DFT of an impulse signal is flat, meaning all frequency components are equally present.

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Positive Frequency

The positive frequency component of a signal in the frequency domain.

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Negative Frequency

The negative frequency component of a signal in the frequency domain, represented symmetrically to the positive frequency.

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Amplitude of Frequency Component

The strength of each frequency component in the frequency domain, represented by the peak height.

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Phase of Frequency Component

The starting point of a frequency component in the time domain, represented by the peak position on the frequency axis.

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What is STFT?

A technique for analyzing signals whose frequency content changes over time, by dividing the signal into overlapping segments and applying a Fourier transform to each segment.

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Why is the STFT needed?

The standard Fourier transform provides frequency information but lacks time resolution. STFT solves this by analyzing smaller segments of the signal, effectively adding a time dimension.

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How does STFT work?

A window function, like the Hamming window, is applied to isolate a small portion of the signal. Then, a Fourier transform is performed on this isolated segment.

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What is a window function?

A function that shapes the signal segment, emphasizing certain parts and suppressing others. It helps to reduce distortion caused by abrupt transitions at the segment boundaries.

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What is a Fourier transform?

A mathematical process that decomposes a signal into its constituent frequencies. This helps to understand the frequency content present in a signal.

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What is window length?

The length of the signal segment used in STFT. A longer window provides better frequency resolution but poorer time resolution.

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What is window overlap?

The amount of overlap between consecutive window segments in STFT. More overlap results in smoother transitions but may increase computation time.

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What is a spectrogram?

A representation of the frequency content of a signal over time, created by performing STFT. Each point in the spectrogram represents the amplitude of a specific frequency at a particular time.

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Study Notes

Sensor Technology

  • Sensor technology encompasses the basics of sensors, resistive sensors, capacitive and inductive sensors, and microphones.
  • Signal analysis involves signals and statistics, number representation, linear systems, Fourier transform, and frequency plots.

Programming

  • MATLAB's primary windows include: command window, workspace, and editor.
  • Arrays are general data structures, whereas matrices are two-dimensional arrays.
  • Parentheses are for indexing and function calls, while square brackets create arrays and matrices.

Lecture 2 - Number representation

  • Integer representation includes unsigned (positive values) and signed (positive and negative).
  • Real numbers, such as floating-point, employ IEEE standards (single and double precision).

Lecture 3 - Linear Systems

  • A system is linear if homogeneity (scaling) and additivity (superposition) are satisfied.
  • Linear time-invariant (LTI) systems are predictable and amenable to Fourier analysis.

Lecture 4 - Capacitive and Inductive Sensors

  • Capacitive and inductive sensors (e.g., humidity sensor, condenser microphone, touch screen)
  • Their parameters change capacitance of a plate capacitor.

Lecture 5 - Microphones

  • Microphone types (e.g., condenser, dynamic, ribbon, carbon) and their advantages and disadvantages.

Lecture 6 - Signals and Statistics

  • Signal analysis defines how one parameter relies on another.
  • Continuous/discrete signals and time/frequency domains.
  • Analog-to-digital converters produce discrete/digitized signals.
  • Sampling: Convert independent variables from continuous to discrete.
  • Quantization: Convert dependent variables from continuous to discrete.

Lecture 7 - Filters

  • Types of filters (e.g., low-pass, high-pass, band-pass, band-reject).
  • Effects of different filters in specific frequency ranges.

Lecture 8 & 9 - FIR and IIR Filters

  • FIR and IIR filters (finite impulse response, infinite impulse response)

MATLAB Code Explanation (Step 1)

  • Data loading uses file paths stored in a cell array for flexibility.
  • File input and error handling are central aspects.
  • String splitting extracts data elements for parsing.

MATLAB Code Explanation (Step 2 - Time Data Editing)

  • Converts time strings into a datetime format for data analysis.
  • Calculates the elapsed time.
  • Converts these to numeric values for data processing.

MATLAB Code Explanation (Step 3 - Data Validation)

  • Plots both raw and filtered data.
  • Identifies noisy data segments.
  • Provides a visual comparison for data analysis.

MATLAB Code Explanation (Step 4)

  • Calculates sampling frequency from time stamps.
  • Converts time stamps into a numerical form (seconds).

MATLAB Code Explanation (Step 5)

  • Removes Direct Current (DC) offset by subtracting the mean from the signal.
  • Centering the signal around zero helps analysis.

MATLAB Code Explanation (Step 6)

  • Computes the Fast Fourier Transform (FFT).
  • Generates frequency vectors for analysis..
  • Isolates positive frequencies.

MATLAB Code Explanation (Step 7)

  • Plotting subplots for comparing the FFTs of unfiltered and filtered signals for easier analysis of the effects of filtering.

MATLAB Code Explanation (Step 8)

  • Identifies peaks in the filtered signal.
  • Marks the peaks and provides useful plotting functions.

MATLAB Code Explanation (Step 9)

  • Identifies peaks in a signal where amplitude is above a threshold..
  • Plotting functions effectively highlight the peaks.
  • Plotting the data with a horizontal reference to aid visual interpretation

MATLAB Code Explanation (Step 10)

  • Calculates the average interval between peaks.
  • Measures the heart rate in beats per minute (BPM).

Questions to Prepare for the Final Exam

  • Explain the overall structure of the code.
  • Detail data loading, validating, and pre-processing steps.
  • Explain the purpose of various MATLAB commands.

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Description

This quiz covers fundamental concepts in sensor technology, including resistive, capacitive, and inductive sensors, as well as signal analysis techniques such as Fourier transform. Additionally, it explores MATLAB programming, focusing on data structures like arrays and matrices and their usage in numerical computations.

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