ESP32: How to output different signals on each DAC channel, where DAC is in Continuous Wave Output mode (Continuous/DMA Mode)?

I want to generate two signals on the DAC outputs of ESP32, the sine and cosine ones, thus shifted by 90 deg. But I have the same signal on both DAC outputs.

From the Espressif documentation I found that The DAC channels can't be registered to continuous mode separately (link to docs)

Moreover, I found from the documentation (dac cont config) such information for DAC configuration:

    cont_cfg = {
        .chan_mask = DAC_CHANNEL_MASK_ALL,
        .desc_num = 2,
        .buf_size = 2048,
        .freq_hz = frequency_convert_Hz,
        .offset = 0,
        .clk_src = DAC_DIGI_CLK_SRC_DEFAULT, // If the frequency is out of range, try 'DAC_DIGI_CLK_SRC_APLL'
        .chan_mode = DAC_CHANNEL_MODE_ALTER,
    };
    /* Assume the data in buffer is 'A B C D E F'
     * DAC_CHANNEL_MODE_SIMUL:
     *      - channel 0: A B C D E F
     *      - channel 1: A B C D E F
     * DAC_CHANNEL_MODE_ALTER:
     *      - channel 0: A C E
     *      - channel 1: B D F
     */

Thus, if I understood correctly, for my task I have to use the ALTER mode .chan_mode = DAC_CHANNEL_MODE_ALTER to put different signals into two DAC channels (channel_mode).

    /* Assume the data in buffer is 'A B C D E F'
     * DAC_CHANNEL_MODE_ALTER:
     *      - channel 0: A C E
     *      - channel 1: B D F
     */

And I have written a function for sine and cosine signals generation, where I used the intersection of these two signals in the same buffer:

void generate_waves(void)
{
    for (int i = 0; i < EXAMPLE_ARRAY_LEN; i++)
    {
        if (i % 2)
        {
            signal_wave[i] = (uint8_t)(amplitude / 2 * (1 + sin(2 * M_PI * i / EXAMPLE_ARRAY_LEN)));
        }
        else
        {
            signal_wave[i] = (uint8_t)(amplitude / 2 * (1 + cos(2 * M_PI * i / EXAMPLE_ARRAY_LEN)));
        }
    }
}

However, no effect. The signals are the same on both DAC outputs!

My example code

The PlatformIO some config:

[env]

platform = https://github.com/Jason2866/platform-espressif32.git
framework = arduino

The main.cpp file:

#include <Arduino.h>

#include "DAC_Continuous_DMA.h"

void setup()
{
  Serial.begin(921600);

  dac_continuous_dma_config(1000);
}

void loop()
{
  // Just for testing
  Serial.printf("Free heap size: %d\n", esp_get_free_heap_size());
  Serial.printf("%s(), core: %d: Running time [s]: %d\n", __func__, xPortGetCoreID(), millis());

  vTaskDelay(pdMS_TO_TICKS(1000));
}

The DAC_Continuous_DMA.h file:

#pragma once
#ifndef DAC_Continuous_DMA_h
#define DAC_Continuous_DMA_h

#include "Arduino.h"
#include <math.h>
#include "freertos/FreeRTOS.h"
#include "freertos/task.h"
#include "soc/dac_channel.h"
#include "driver/dac_continuous.h"

#include "soc/sens_reg.h"

#define EXAMPLE_ARRAY_LEN 512     // Length of wave array
#define EXAMPLE_DAC_AMPLITUDE 255 // Amplitude of DAC voltage. If it's more than 256 will causes

#define CONST_2_PI 6.2832 // 2 * PI

_Static_assert(EXAMPLE_DAC_AMPLITUDE < 256, "The DAC accuracy is 8 bit-width, doesn't support the amplitude beyond 255");

dac_continuous_config_t cont_cfg;

uint8_t signal_wave[EXAMPLE_ARRAY_LEN]; // Used to store sine wave values
uint8_t amplitude = EXAMPLE_DAC_AMPLITUDE;

dac_continuous_handle_t cont_handle = NULL;

void generate_waves(void)
{
    for (int i = 0; i < EXAMPLE_ARRAY_LEN; i++)
    {
        if (i % 2)
        {
            signal_wave[i] = (uint8_t)(amplitude / 2 * (1 + sin(2 * M_PI * i / EXAMPLE_ARRAY_LEN)));
        }
        else
        {
            signal_wave[i] = (uint8_t)(amplitude / 2 * (1 + cos(2 * M_PI * i / EXAMPLE_ARRAY_LEN)));
        }
    }
}

void dac_continuous_dma_config(uint32_t frequency_Hz = 1000)
{
    generate_waves();

    cont_cfg = {
        .chan_mask = DAC_CHANNEL_MASK_ALL,
        .desc_num = 2,
        .buf_size = 2048,
        .freq_hz = EXAMPLE_ARRAY_LEN * frequency_Hz / 2,
        .offset = 0,
        .clk_src = DAC_DIGI_CLK_SRC_DEFAULT, // If the frequency is out of range, try 'DAC_DIGI_CLK_SRC_APLL'
        .chan_mode = DAC_CHANNEL_MODE_ALTER,
    };
    /* Assume the data in buffer is 'A B C D E F'
     * DAC_CHANNEL_MODE_SIMUL:
     *      - channel 0: A B C D E F
     *      - channel 1: A B C D E F
     * DAC_CHANNEL_MODE_ALTER:
     *      - channel 0: A C E
     *      - channel 1: B D F
     */

    ESP_ERROR_CHECK(dac_continuous_new_channels(&cont_cfg, &cont_handle));
    ESP_ERROR_CHECK(dac_continuous_enable(cont_handle));
    ESP_ERROR_CHECK(dac_continuous_write_cyclically(cont_handle, (uint8_t *)signal_wave, EXAMPLE_ARRAY_LEN, NULL));

}

#endif // DAC_Continuous_DMA_h

The problem/question summary:

How to output different signals on each DAC channel, where DAC is in Continuous Wave Output mode (Continuous/DMA Mode)?

Thanks for your comments and help!