 # What happens when to the spectrum of a signal when it is sampled?

What happens when to the spectrum of a signal when it is sampled? Sampling produces a larger number of frequency components not in the original spectrum, even components having negative frequency. The sampled signal has a spectrum that is periodic at the sampling frequency (20 Hz) and has an even symmetry about 0.0 Hz, as well as symmetry about the sampling frequency, fs.

What will happen if we sample a signal with under sampling condition? When undersampling a real-world signal, the sampling circuit must be fast enough to capture the highest signal frequency of interest. If the sampling theorem is interpreted as requiring twice the highest frequency, then the required sampling rate would be assumed to be greater than the Nyquist rate 216 MHz.

What does the spectrum of a signal tell us? The signal spectrum describes a signal’s magnitude and phase characteristics as a function of frequency. The system spectrum describes how the system changes signal magnitude and phase as a function of frequency. For example, at around 100 Hz the transfer function has a magnitude value of around 0.707.

How may the original signal recovered from the sampled signal? The original signal is recoverable from its sampled form when the highest frequency component is less than the Nyquist frequency, ωs/2. It has frequency components below ωs that overlap with the positive frequency components of V(ω). These are negative frequencies in V(ω) shifted up in frequency by ωs.

## What happens when to the spectrum of a signal when it is sampled? – Related Questions

### When a signal is sampled what happens to its spectrum?

The sampled signal has a spectrum that is periodic at the sampling frequency (20 Hz) and has an even symmetry about 0.0 Hz, as well as symmetry about the sampling frequency, fs. Since the sampled spectrum is periodic, it goes on forever and only a portion of it can be shown.

### Why is sampling important in signal processing?

To convert a signal from continuous time to discrete time, a process called sampling is used. The value of the signal is measured at certain intervals in time. If the signal contains high frequency components, we will need to sample at a higher rate to avoid losing information that is in the signal.

### What is the effect of under sampling?

Undersampling leads to three significant complications: (1) MTF and NPS do not behave as transfer amplitude and variance, respectively, of a single sinusoid, (2) the response of a digital system to a delta function is not spatially invariant and therefore does not fulfill certain technical requirements of classical

### What happens if you oversample a signal?

Quantization noise is a rounding error created during digital sampling that produces a very low-level noise correlated to the audio signal. Oversampling can shift this noise into higher frequency ranges, where they can be filtered out or become less audible to the human ear.

### What is the limitation of under sampling?

The major drawback of random undersampling is that this method can discard potentially useful data that could be important for the induction process.

### Why is frequency spectrum important?

Having more spectrum helps operators to deliver this better user experience. In particular, aggregating spectrum into larger downlink carriers raises peak data speeds but also more generally helps to provide the higher average speeds valued by many users.

### Why do we need frequency spectrum?

Spectrum is a range of electromagnetic radio frequencies used for transmission of voice, data and images. Mobile telecom operators send and receive frequencies to enable communication between two phones. The defence services and railways also use the spectrum .

### What is the use of frequency spectrum?

The RF spectrum is divided into small chunks for a huge number of applications such as AM and FM radio, television, cellular networks, walkie-talkies, satellite communications, military applications, and even to send and receive signals into outer space.

### Which type of filter can be used to recover the original signal from the sampled signal?

low pass filter 18 used to recover original signal from its samples. This also called interpolation filter. use of low-pass filter, there is sharp- change in response at cut-off frequency, that emolitude response becomes suddenly zero teut-off frequency which is not possible prac- aliy.

### How do you reconstruct a signal from its samples?

The reconstruction process consists of replacing each sample by a sinc function, centered at the time of the sample and scaled by the sample value x(nT) times 2fc/ fs and adding all the functions so created. Suppose the signal is sampled at exactly Nyquist rate fs= 2fm, Then fm= fs/2 = fs- fm and Fm= 1/2 = 1- Fm.

### Which filter is used to get back the original signal from sampled signal?

The correct answer is option A. In order to get back the original signal from sampled signal , it is necessary to use low pass filter. Low pass filter removes the components sending high frequency signals, smoothens edges and reconstructs the samples signal to give back original signal as output.

### How do you find the spectrum of a signal?

Frequency spectrum of a signal is the range of frequencies contained by a signal. For example, a square wave is shown in Fig. 3.5A. It can be represented by a series of sine waves, S(t) = 4A/π sin(2πft) + 4A/3π sin(2π(3f)t) + 4A/5π sin(2π(5f)t + …)

### What are the spectrum and bandwidth of a signal?

The spectrum of a signal is the range of frequencies contained in the signal. The bandwidth is the difference between the lowest and highest frequency in the spectrum. It is therefore the width of the spectrum and is a measure of the information carrying capacity of the signal.

### What is the spectrum of a sine wave?

The spectrum of a sine wave is a single point at the frequency of the sine wave. The spectrum of white noise is a line covering all frequencies. The cochlea breaks the waveform at the ear down into its component sine waves – frequency analysis. Hair cells in the cochlea respond to these component frequencies.

### Why is sampling important?

Sampling saves money by allowing researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling, because it lowers the cost associated with finding people and collecting data from them.

### What is the importance of sampling of signals in electronic systems?

DSP systems

Sampling is the process of taking an analog signal and converting it to discrete numbers. The sampling frequency (or sampling rate) is how many times per second the signal will be sampled. This is important because it restricts the highest frequency that can be present in a signal.

### What is sampling in digital signal processing?

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal). A sample is a value or set of values at a point in time and/or space.

### What is the effect of undersampling Mcq?

Explanation: Undersampling causes aliasing which at the output of the ADC results in a wave with much lower frequency than the original signal. To reduce aliasing effects, antialiasing filters are used which acts as a low pass filter.

### What is undersampling explain with an example?

Random undersampling involves randomly selecting examples from the majority class and deleting them from the training dataset. In the random under-sampling, the majority class instances are discarded at random until a more balanced distribution is reached.

### How does oversampling reduce noise?

This technique decreases noise in the bandwidth of interest by “shifting” it to higher frequencies where it has less effect on your signals of interest. This in effect “shifts” quantization into higher frequencies. Oversampling does not decrease the total noise power, it simply distributes it at higher frequencies.

### What is SMOTETomek?

SMOTETomek is somewhere upsampling and downsampling. SMOTETomek is a hybrid method which is a mixture of the above two methods, it uses an under-sampling method (Tomek) with an oversampling method (SMOTE). Class 0 has been downsampled from 500 to 472 and class 1 has been upsampled from 268 to 472.