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UPDATE 1: As requested doing a spreadsheet of different frequencies and a block diagram and a physical setup to show you guys.

#define ARM_MATH_CM7

#include "main.h"

#include "arm_math.h"


void init_Clock(void);
void init_I2S(void);
void init_Debugging(void);
void init_Interrupt(void);
void init_SpeedTest(void);

int32_t RxBuff[4];
int32_t TxBuff[4];
uint8_t TC_Callback = 0;
uint8_t HC_Callback = 0;

char uartBuff[8];
 float32_t iir_coeffs[5] = {0.00102f, 0.002041f, 0.00102f, 1.908f, -0.9116f}; //B0, B1, B2, A1, A2
float32_t iir_mono_state[4];

float32_t Rx_Buff_f[4];
float32_t Rx_Buff_f_out[4];


arm_biquad_casd_df1_inst_f32 monoChannel;


void DMA1_Stream0_IRQHandler(void) {

    if (((DMA1 -> LISR) & (DMA_LISR_TCIF0)) != 0){
        DMA1 -> LIFCR |= DMA_LIFCR_CTCIF0;
        TC_Callback = 1;
    }

    else if (((DMA1 -> LISR) & (DMA_LISR_HTIF0)) != 0){
         DMA1 -> LIFCR |= DMA_LIFCR_CHTIF0;
         HC_Callback = 1;

    }
}

int main(void) {

    init_Clock();
    init_I2S();
    //init_Debugging();
    init_Interrupt();
    //init_SpeedTest();
    arm_biquad_cascade_df1_init_f32(&monoChannel, 1, iir_coeffs, iir_mono_state);

  while (1)
  {

      if (HC_Callback == 1){

         // GPIOA->BSRR |= GPIO_BSRR_BS3_HIGH;

          for (int i = 0; i < 2; i++){
              Rx_Buff_f[i] = (float32_t)RxBuff[i];
          }

          arm_biquad_cascade_df1_f32(&monoChannel, Rx_Buff_f, Rx_Buff_f_out, 2);

          for (int i = 0; i < 2; i++){
                TxBuff[i] = (int32_t)Rx_Buff_f_out[i];
            }

          HC_Callback = 0;

      } else  if (TC_Callback == 1){


        //  GPIOA->BSRR |= GPIO_BSRR_BR3_LOW;


          for (int i = 2; i < 4; i++){
               Rx_Buff_f[i] = (float32_t)RxBuff[i];
            }

                  arm_biquad_cascade_df1_f32(&monoChannel, &Rx_Buff_f[2], &Rx_Buff_f_out[2], 2);

                  for (int i = 2; i < 4; i++){
                        TxBuff[i] =  (int32_t)Rx_Buff_f_out[i];
                    }



          TC_Callback = 0;

      }



  }

}

#define ARM_MATH_CM7

#include "main.h"

#include "arm_math.h"


void init_Clock(void);
void init_I2S(void);
void init_Debugging(void);
void init_Interrupt(void);
void init_SpeedTest(void);

int32_t RxBuff[4];
int32_t TxBuff[4];
uint8_t TC_Callback = 0;
uint8_t HC_Callback = 0;

char uartBuff[8];
 float32_t iir_coeffs[5] = {0.00102f, 0.002041f, 0.00102f, 1.908f, -0.9116f}; //B0, B1, B2, A1, A2
float32_t iir_mono_state[4];

float32_t Rx_Buff_f[4];
float32_t Rx_Buff_f_out[4];


arm_biquad_casd_df1_inst_f32 monoChannel;


void DMA1_Stream0_IRQHandler(void) {

    if (((DMA1 -> LISR) & (DMA_LISR_TCIF0)) != 0){
        DMA1 -> LIFCR |= DMA_LIFCR_CTCIF0;
        TC_Callback = 1;
    }

    else if (((DMA1 -> LISR) & (DMA_LISR_HTIF0)) != 0){
         DMA1 -> LIFCR |= DMA_LIFCR_CHTIF0;
         HC_Callback = 1;

    }
}

int main(void) {

    init_Clock();
    init_I2S();
    //init_Debugging();
    init_Interrupt();
    //init_SpeedTest();
    arm_biquad_cascade_df1_init_f32(&monoChannel, 1, iir_coeffs, iir_mono_state);

  while (1)
  {

      if (HC_Callback == 1){

         // GPIOA->BSRR |= GPIO_BSRR_BS3_HIGH;

          for (int i = 0; i < 2; i++){
              Rx_Buff_f[i] = (float32_t)RxBuff[i];
          }

          arm_biquad_cascade_df1_f32(&monoChannel, Rx_Buff_f, Rx_Buff_f_out, 2);

          for (int i = 0; i < 2; i++){
                TxBuff[i] = Rx_Buff_f_out[i];
            }

          HC_Callback = 0;

      } else  if (TC_Callback == 1){


        //  GPIOA->BSRR |= GPIO_BSRR_BR3_LOW;


          for (int i = 2; i < 4; i++){
               Rx_Buff_f[i] = (float32_t)RxBuff[i];
            }

                  arm_biquad_cascade_df1_f32(&monoChannel, &Rx_Buff_f[2], &Rx_Buff_f_out[2], 2);

                  for (int i = 2; i < 4; i++){
                        TxBuff[i] = Rx_Buff_f_out[i];
                    }



          TC_Callback = 0;

      }



  }

}

Bode plot from Oscilloscope with the biquad filter:

CODE:

#define ARM_MATH_CM7

#include "main.h"

#include "arm_math.h"


void init_Clock(void);
void init_I2S(void);
void init_Debugging(void);
void init_Interrupt(void);
void init_SpeedTest(void);

int32_t RxBuff[4];
int32_t TxBuff[4];
uint8_t TC_Callback = 0;
uint8_t HC_Callback = 0;

char uartBuff[8];
 float32_t iir_coeffs[5] = {0.00102f, 0.002041f, 0.00102f, 1.908f, -0.9116f}; //B0, B1, B2, A1, A2
float32_t iir_mono_state[4];

float32_t Rx_Buff_f[4];
float32_t Rx_Buff_f_out[4];


arm_biquad_casd_df1_inst_f32 monoChannel;


void DMA1_Stream0_IRQHandler(void) {

    if (((DMA1 -> LISR) & (DMA_LISR_TCIF0)) != 0){
        DMA1 -> LIFCR |= DMA_LIFCR_CTCIF0;
        TC_Callback = 1;
    }

    else if (((DMA1 -> LISR) & (DMA_LISR_HTIF0)) != 0){
         DMA1 -> LIFCR |= DMA_LIFCR_CHTIF0;
         HC_Callback = 1;

    }
}

int main(void) {

    init_Clock();
    init_I2S();
    //init_Debugging();
    init_Interrupt();
    //init_SpeedTest();
    arm_biquad_cascade_df1_init_f32(&monoChannel, 1, iir_coeffs, iir_mono_state);

  while (1)
  {

      if (HC_Callback == 1){

         // GPIOA->BSRR |= GPIO_BSRR_BS3_HIGH;

          for (int i = 0; i < 2; i++){
              Rx_Buff_f[i] = (float32_t)RxBuff[i];
          }

          arm_biquad_cascade_df1_f32(&monoChannel, Rx_Buff_f, Rx_Buff_f_out, 2);

          for (int i = 0; i < 2; i++){
                TxBuff[i] = (int32_t)Rx_Buff_f_out[i];
            }

          HC_Callback = 0;

      } else  if (TC_Callback == 1){


        //  GPIOA->BSRR |= GPIO_BSRR_BR3_LOW;


          for (int i = 2; i < 4; i++){
               Rx_Buff_f[i] = (float32_t)RxBuff[i];
            }

                  arm_biquad_cascade_df1_f32(&monoChannel, &Rx_Buff_f[2], &Rx_Buff_f_out[2], 2);

                  for (int i = 2; i < 4; i++){
                        TxBuff[i] =  (int32_t)Rx_Buff_f_out[i];
                    }



          TC_Callback = 0;

      }



  }

}