Finally, we must write a function to \"mix\" all of the outputs of our ADSR bloc

Question

Finally, we must write a function to "mix" all of the outputs of our ADSR blocks. This will allow us to make more complex combinations of different instruments or even create a chord (multiple notes) from the same instrument model. Our final mix y(t) can be written as a linear combination of N amplitude modulated signals, where ci is the ith mixing coefficient and ai(t) and xi(t) are the corresponding ADSR envelope and output from the ith additive synthesis block. Write a function that accepts ADSR modulated signals and mixes them by forming a weighted linear combination of the signals. Your function must be able to mix together an arbitrary number of signals (of the same length) with different coefficients. After mixing the signals, rescale the signal (between +/- 1) to ensure that clipping does not occur during playback.

Explanation / Answer

The Mixer block models a mixer in the SimRF circuit-envelope simulation environment. For more information about simulating RF systems, see the example, Minimize Computations for RF Simulations. To perform frequency mixing, the block: Multiplies the signals at the input ports together. Places the modulations of the mixed signals on environment carriers. Applies a conversion gain. For example, for input signals Vin = Aincos(?int) and VLO = ALOcos(?LOt), the mixer multiplies the signals at the input ports: The block places the modulations of the mixed signals on the carriers ?in + ?LO and ?in – ?LO. If ?in + ?LO or ?in – ?LO is not specified in the Carrier frequencies parameter of the SimRF Parameters block, the mixer does not output a signal at that carrier. To model linear conversion gain, the mixer implements the relation between the voltage signal Vi of each mixing product and the voltage signal Vo at the output of the mixer. To model nonlinear conversion gain, The mixer implements the relation between the voltage signal Vi of each mixing product and the voltage signal Vo at the output of the mixer. The block derives the polynomial coefficients from specified IP2 and IP3 parameters of the mixer: Input IP2 and input IP3 are the ratio of OIP2 and OIP3 to a12. The remaining polynomial coefficients a2 and a3 are defined by the input modulation Ai,IP2 and Ai,IP3: Models that contain SimRF Amplifier and Mixer blocks generate files at update time. Before you can successfully update and run models with these blocks, you have to set up a compiler by running mex -setup. By default, SimRF software generates files in the current MATLAB folder. However, you can change the output location for these files by specifying a cache folder in the Simulink Preferences dialog. To specify a cache folder: On the Home tab, in the Environment section, click Preferences. Click Simulink, then click Launch Simulink Preferences. Specify the Simulink cache folder parameter. Dialog Box and Parameters Source of conversion gain Specify the source parameter of the conversion gain as: Available power gain — The block uses the value of the Available power gain parameter. Available power can be measured by implementing a conjugate match between the output and load. Open circuit voltage gain — The block uses the value of the Open circuit voltage gain parameter. Open circuit voltage gain can be measured with an open circuit at the output. The default value of this parameter is Available power gain. Available power gain When Source of conversion gain is Available power gain, specify the linear gain of the mixer. Specify the units from the corresponding drop-down list. If you specify the units as None, the gain must be positive. The default value of this parameter is 0 dB. Open circuit voltage gain When Source of conversion gain is Open circuit voltage gain, specify the open circuit voltage gain of the mixer. Specify the units from the corresponding drop-down list. If you specify the units as None, the gain must be positive. The default value of this parameter is 0 dB. Input impedance (ohms) Specify the scalar impedance at the In port of the mixer. The default value of this parameter is 50 ?. Output impedance (ohms) Specify the scalar impedance at the Out port of the mixer. The default value of this parameter is 50 ?. LO impedance (ohms) Specify the scalar impedance at the LO port of the mixer. The default value of this parameter is Inf ?. Source of cubic polynomial Specify how the block calculates the nonlinear effects of the mixer as: Derived from intercept points — Specify the IP2 and IP3 parameters, from which the block defines a cubic polynomial. User—specified — Specify a Cubic polynomial coefficients vector to define the cubic polynomial directly. Intercept points at Specify the IP2 and IP3 parameters as either Input or Output intercept points. IP2 Specify the second-order intercept point of the mixer. The default value is inf. This parameter applies only when you set Source of cubic polynomial to Derived from intercept points. IP3 Specify the third-order intercept point of the mixer. The default value is inf. This parameter applies only when you set Source of cubic polynomial to Derived from intercept points. Noise figure (dB) Specify the noise figure of the mixer. The default value of this parameter is 0 dB. To model noise in a SimRF model with a Noise, Amplifier, or Mixer block, you must select the Simulate noise check box in the SimRF Parameters block dialog box. Cubic polynomial coefficients Specify the coefficients of the polynomial a0 + a1V1 + a2V22 + a3V33. The elements of the vector are [a0,a1,a2,a3]. Trailing zeroes can be omitted; for example, if a3 = 0, [a0,a1,a2] defines the same polynomial as [a0,a1,a2,0]. The default value of this parameter is [0 1], corresponding to the polynomial a1V1. Specifying a polynomial overrides the available power gain or open circuit voltage gain since the polynomial contains the term a1. Ground and hide negative terminals Select this check box to internally ground and hide the negative terminals of the block. Clear the check box to expose the negative terminals, allowing you to connect them to other parts of your model. By default, this check box is selected.

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