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1) This document discusses the discrete-time Fourier transform (DTFT), including its derivation, properties, and examples. 2) Two examples are provided: the DTFT of a decaying exponential is another decaying exponential, and the DTFT of a rectangular pulse of length N is a sinc function. 3) The key properties of the DTFT discussed are its convolution and multiplication properties, and that periodic signals can be represented using the DTFT.
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The document discusses properties of the discrete-time Fourier transform (DTFT) and discrete Fourier transform (DFT), including:
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reduced to the processing separately the splitting-signals by the shifted discrete Fourier transforms
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detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
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### How TDM Works
1. **Time Slots Allocation**: The core principle of TDM is to assign distinct time slots to each signal. During each time slot, the respective signal is transmitted, and then the process repeats cyclically. For example, if there are four signals to be transmitted, the TDM cycle will divide time into four slots, each assigned to one signal.
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3. **Frame Structure**: TDM data is organized into frames, where each frame consists of a set of time slots. Each frame is repeated at regular intervals, ensuring continuous transmission of data streams. The frame structure helps in managing the data streams and maintaining the synchronization between the transmitter and receiver.
4. **Multiplexer and Demultiplexer**: At the transmitting end, a multiplexer combines multiple input signals into a single composite signal by assigning each signal to a specific time slot. At the receiving end, a demultiplexer separates the composite signal back into individual signals based on their respective time slots.
### Types of TDM
1. **Synchronous TDM**: In synchronous TDM, time slots are pre-assigned to each signal, regardless of whether the signal has data to transmit or not. This can lead to inefficiencies if some time slots remain empty due to the absence of data.
2. **Asynchronous TDM (or Statistical TDM)**: Asynchronous TDM addresses the inefficiencies of synchronous TDM by allocating time slots dynamically based on the presence of data. Time slots are assigned only when there is data to transmit, which optimizes the use of the communication channel.
### Applications of TDM
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- **Digital Audio and Video Broadcasting**: TDM is used in broadcasting systems to transmit multiple audio or video streams over a single channel, ensuring efficient use of bandwidth.
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- 5. Examples
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- 7. EE-2027 SaS, L11 Example 2: Rectangular Pulse • Consider the rectangular pulse • and the Fourier transform is > ≤ = 1 1 | | 0 | | 1 ] [ N n N n n x ) 2 / sin( )) 2 / 1 ( sin( 1 1 ) ( 1 2 / 2 / ) 2 / 1 ( ) 2 / 1 ( ) 1 2 ( ) 2 / 1 ( ) 2 / 1 ( 2 0 1 1 1 1 1 1 1 1 ω ω ω ω ω ω ω ω ω ω ω ω ω ω + = − − = − − = = = − + − + − + − + = − − = − ∑ ∑ N e e e e e e e e e e e e X j j N j N j j N j j N j N m m j N j N N n n j j N1=2
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- 12. DTFT of Periodic Signals Recall the following DTFT pair: Represent periodic signal x[n] in terms of DTFS:
- 17. Next Class