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eces-lab7-Vy - Abstract The band pass FIR is one of the...

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Abstract The band pass FIR is one of the methods that help to extract information from sinusoidal signals. In this lab, students will distract information from piano notes. This experiment teaches the student how to characterize a filter by knowing how it reacts to different frequency components in the input. The main purpose of this experiment is to design and implement several FIR filters in Matlab tools. The firlt and conv functions were used to obtain the necessary frequency response. Introduction The goal of this lab experiment is to understand how to extract information from sinusoidal signals or specifically piano notes. The method that one can use in this lab is the FIR filters in Matlab. Moreover, the tool can also use to determine the note that was played. Fortunately, students are only required to find which octave the note is in. Finally, student will
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learn how to characterize a filter by inspecting the way it reacts to different frequency components of the input. In the first part of the experiment, a Hamming bandpass filter was generated that passed a frequency component at w = 0.25π, 0.4 π , 0.5 π , 0.75 π . The passband width for L = 41 was calculated to be 0.282. When the length is doubled, the width is halved, and when the length is halved, the width is doubled. The components at w = ±0.25π are within the bounds of the length- 41 passband width and that magnitude of this component is greater than the magnitude of the components at the edge of the passband filter. In the piano note decoding, MatLab’s max function was used to measure the peak value of the unscaled frequency response. For Octave #6, the length L is 108. There is obviously a transient effect at the transitions. This is due to the start-up of each FIR filter as it encounters a new sinusoid. . Looking over the output graph, the transient effect last around 10 or 0.01 seconds. This seems to be the case for all the filters in the filter bank. The final objective of this experiment is to detect which octave contains the notes. In order for us to do this, we need a score function, which will help to comparing the scores to a threshold. This will give an output of zero or one. Theory The "ideal" band-pass filter can be used to isolate the component of a time series that lies within a particular band of frequencies, but applying this filter requires a data set of infinite length. A band pass filter is designed to pass all frequencies within a band of frequencies, such that there is a high and low cutoff. The frequency band is determined by the design of the circuit, which dictates the given cutoff frequencies. Unlike high pass and low pass filtering, band pass filters have two distinct cutoff frequencies that provide the high and low ends of the range. Any frequency falling outside this range will be attenuated. Band pass filters can be formed by
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cascading a high pass and low pass filter together to cutoff both the low and the high frequencies surrounding the desired range. Typically, this results in a circuit less suitable for specific design tweaking, so designs typically are made using a single circuit instead of two cascaded designs.
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