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To find the functions you will use to send and read messages from the ADC, either find the stm32f0xx_hal_spi.h file in the Drivers->STM32F0xx_HAL_Driver->Inc directory and read the function prototypes at the bottom or visit the HAL User Manual and look for the SPI input and output functions (IO Operations).
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Don’t forget that the ADC requires specific behavior for the CS line that is connected to the GPIO pin you set. Information for controlling a GPIO pin can be found in the HAL User Manual.
Converting ADC value to PWM signal
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Look at the HAL_TIM_ and __HAL_TIM_ functions to access the timer. The HAL User Manual will be particularly useful here.
For SPI communication look at the SPI IO operation function in the HAL User Manual.
The electrical schematic is useful for determining which pins should be configured to which peripheral.
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